One, I do not see where the First Amendment is involves, since a HOA is not a governmental agency.
As for the Freedom to Display the American Flag Act of 2005, let us have the whole act (section 1 is the short title, Section 2 is definitions):
Section 3. RIGHT TO DISPLAY THE FLAG OF THE UNITED STATES.
A condominium association, cooperative association, or residential real estate management association may not adopt or enforce any policy, or enter into any agreement, that would restrict or prevent a member of the association from displaying the flag of the United States on residential property within the association with respect to which such member has a separate ownership interest or a right to exclusive possession or use.
Section 4. LIMITATIONS.
Nothing in this Act shall be considered to permit any display or use that is inconsistent with--
(1) any provision of chapter 1 of title 4, United States Code, or any rule or custom pertaining to the proper display or use of the flag of the United States (as established pursuant to such chapter or any otherwise applicable provision of law); or
(2) any reasonable restriction pertaining to the time, place, or manner of displaying the flag of the United States necessary to protect a substantial interest of the condominium association, cooperative association, or residential real estate management association.
Emphasis added by me.
Hence, an HOA may still place reasonable restrictions on the manner of displaying the flag, which would probably include outsized flagpoles.