Quick answer please!

If the Bylaws say you may not hang anything from your balcony.....can displaying the American flag on Memorial Day only for the one day be the exception? I find nothing in the bylaws referring to the flag for this particular day or any other day for that matter.
Thanks!

If your balcony is exclusive use (or limited use) common area, the HOA probably can tell you you may not hang, fly or etc., anything from your balcony rails. Most condo HOAs don't permit anything to be attached to the railings, walls, ceilings of balconies.. The reason is penetration into the rails or walls or ceiling can permit water intrusion into the common area of the HOA, which is bad thing.

You can put a flag in the window of your home.

What donor rules say?

Read TimB4's linked citation in particular. For the sake of argument, let's assume your condo's covenants do restrict flag flying and in a manner consistent with the Michigan Condo Act and the federal "Freedom to Display the American Flag" statute. Condominium associations and HOAs still have to issue warnings before fining. If you want to hang the flag today (Memorial Day, 2020), go for it. At most, you should only get a warning.

Please look into the Federal law that allows the American flag to be displayed and HOA's cannot limit it.

In CA, ppl may fly an official USA flag on their exclusive (limited) use common area balcony. (But it can't be attached in any way that penetrates the railing wall, etc.).

A neighbor in our condo high rise had a US flag with a huge yellow cross embossed on it, and had to take it down as it was not an "official" US flag.

This may be national legislation, too.

Check Michigan state law or call your Fed Congressman's office for Fed law.

This is Florida law
720.304 Right of owners to peaceably assemble; display of flag; SLAPP suits prohibited.—
(1) All common areas and recreational facilities serving any homeowners’ association shall be available to parcel owners in the homeowners’ association served thereby and their invited guests for the use intended for such common areas and recreational facilities. The entity or entities responsible for the operation of the common areas and recreational facilities may adopt reasonable rules and regulations pertaining to the use of such common areas and recreational facilities. No entity or entities shall unreasonably restrict any parcel owner’s right to peaceably assemble or right to invite public officers or candidates for public office to appear and speak in common areas and recreational facilities.
(2)(a) Any homeowner may display one portable, removable United States flag or official flag of the State of Florida in a respectful manner, and one portable, removable official flag, in a respectful manner, not larger than 41/2 feet by 6 feet, which represents the United States Army, Navy, Air Force, Marine Corps, or Coast Guard, or a POW-MIA flag, regardless of any covenants, restrictions, bylaws, rules, or requirements of the association.
(b) Any homeowner may erect a freestanding flagpole no more than 20 feet high on any portion of the homeowner’s real property, regardless of any covenants, restrictions, bylaws, rules, or requirements of the association, if the flagpole does not obstruct sightlines at intersections and is not erected within or upon an easement. The homeowner may further display in a respectful manner from that flagpole, regardless of any covenants, restrictions, bylaws, rules, or requirements of the association, one official United States flag, not larger than 41/2 feet by 6 feet, and may additionally display one official flag of the State of Florida or the United States Army, Navy, Air Force, Marines, or Coast Guard, or a POW-MIA flag. Such additional flag must be equal in size to or smaller than the United States flag. The flagpole and display are subject to all building codes, zoning setbacks, and other applicable governmental regulations, including, but not limited to, noise and lighting ordinances in the county or municipality in which the flagpole is erected and all setback and locational criteria contained in the governing documents.
(c) This subsection applies to all community development districts and homeowners’ associations, regardless of whether such homeowners’ associations are authorized to impose assessments that may become a lien on the parcel.
(3) Any owner prevented from exercising rights guaranteed by subsection (1) or subsection (2) may bring an action in the appropriate court of the county in which the alleged infringement occurred, and, upon favorable adjudication, the court shall enjoin the enforcement of any provision contained in any homeowners’ association document or rule that operates to deprive the owner of such rights.
(4) It is the intent of the Legislature to protect the right of parcel owners to exercise their rights to instruct their representatives and petition for redress of grievances before the various governmental entities of this state as protected by the First Amendment to the United States Constitution and s. 5, Art. I of the State Constitution. The Legislature recognizes that “Strategic Lawsuits Against Public Participation” or “SLAPP” suits, as they are typically called, have occurred when members are sued by individuals, business entities, or governmental entities arising out of a parcel owner’s appearance and presentation before a governmental entity on matters related to the homeowners’ association. However, it is the public policy of this state that government entities, business organizations, and individuals not engage in SLAPP suits because such actions are inconsistent with the right of parcel owners to participate in the state’s institutions of government. Therefore, the Legislature finds and declares that prohibiting such lawsuits by governmental entities, business entities, and individuals against parcel owners who address matters concerning their homeowners’ association will preserve this fundamental state policy, preserve the constitutional rights of parcel owners, and assure the continuation of representative government in this state. It is the intent of the Legislature that such lawsuits be expeditiously disposed of by the courts.
(a) As used in this subsection, the term “governmental entity” means the state, including the executive, legislative, and judicial branches of government, the independent establishments of the state, counties, municipalities, districts, authorities, boards, or commissions, or any agencies of these branches which are subject to chapter 286.
(b) A governmental entity, business organization, or individual in this state may not file or cause to be filed through its employees or agents any lawsuit, cause of action, claim, cross-claim, or counterclaim against a parcel owner without merit and solely because such parcel owner has exercised the right to instruct his or her representatives or the right to petition for redress of grievances before the various governmental entities of this state, as protected by the First Amendment to the United States Constitution and s. 5, Art. I of the State Constitution.
(c) A parcel owner sued by a governmental entity, business organization, or individual in violation of this section has a right to an expeditious resolution of a claim that the suit is in violation of this section. A parcel owner may petition the court for an order dismissing the action or granting final judgment in favor of that parcel owner. The petitioner may file a motion for summary judgment, together with supplemental affidavits, seeking a determination that the governmental entity’s, business organization’s, or individual’s lawsuit has been brought in violation of this section. The governmental entity, business organization, or individual shall thereafter file its response and any supplemental affidavits. As soon as practicable, the court shall set a hearing on the petitioner’s motion, which shall be held at the earliest possible time after the filing of the governmental entity’s, business organization’s or individual’s response. The court may award the parcel owner sued by the governmental entity, business organization, or individual actual damages arising from the governmental entity’s, individual’s, or business organization’s violation of this section. A court may treble the damages awarded to a prevailing parcel owner and shall state the basis for the treble damages award in its judgment. The court shall award the prevailing party reasonable attorney’s fees and costs incurred in connection with a claim that an action was filed in violation of this section.
(d) Homeowners’ associations may not expend association funds in prosecuting a SLAPP suit against a parcel owner.
(5)(a) Any parcel owner may construct an access ramp if a resident or occupant of the parcel has a medical necessity or disability that requires a ramp for egress and ingress under the following conditions:
1. The ramp must be as unobtrusive as possible, be designed to blend in aesthetically as practicable, and be reasonably sized to fit the intended use.
2. Plans for the ramp must be submitted in advance to the homeowners’ association. The association may make reasonable requests to modify the design to achieve architectural consistency with surrounding structures and surfaces.
(b) The parcel owner must submit to the association an affidavit from a physician attesting to the medical necessity or disability of the resident or occupant of the parcel requiring the access ramp. Certification used for s. 320.0848 shall be sufficient to meet the affidavit requirement.
(6) Any parcel owner may display a sign of reasonable size provided by a contractor for security services within 10 feet of any entrance to the home.
History.—s. 36, ch. 92-49; s. 51, ch. 2000-258; s. 1, ch. 2002-50; s. 19, ch. 2004-345; s. 16, ch. 2004-353; s. 1, ch. 2008-45; s. 23, ch. 2010-174.
Note.—Former s. 617.304.

Please do some research before posting. There are limits to what can be displayed where, and claiming an HOA "cannot limit it" is simple not true. "It depends" is the correct answer.