I’ll concede the point. Never looked at it that way.

Yeah, but the 21st specifically mentions the 18th.

That goes to the question of how to interpret the 21st Amendment, not its constitutionality. An identically worded statute purporting to repeal the 18th Amendment would clearly have been unconstitutional. However, the fact that the new amendment does not directly address the First Amendment, or even repeal it outright as to flag desecration as such. Rather, it merely grants Congress the power to prohibit the desecration of the U.S. flag. To the extent the courts can go on enforcing their prior First Amendment cases without violating the new amendment, they will. That means a state law similar to the one struck down in Texas v. Johnson will still be held unconstitutional, as will any federal law aimed at protecting any other flag.

Note more generally that if your theory were valid that a duly enacted constitutional amendment could itself be “unconstitutional,” this would prove that every constitutional amendment, or at least every substantive one, is also “unconstitutional.” Show me a constitutional amendment that doesn’t “violate” the Constitution that existed when it was enacted, and I’ll show you a constitutional amendment that doesn’t do anything at all.

Does “Congress shall make no law” and “shall not be infringed” imply that Congress does not have the power to amend those amendments?

Nah. When in doubt, watch that old Simpsons episode with the Schoolhouse Rock parody. Constitutional amendments limit what Congress can do by ordinary legislation, but they pose no bar whatsoever to future constitutional amendments. The only limits on that are found in Article 5, which provides “that no Amendment which may be made prior to the Year One thousand eight hundred and eight shall in any Manner affect the first and fourth Clauses in the Ninth Section of the first Article; and that no State, without its Consent, shall be deprived of its equal Suffrage in the Senate.” Anything else is fair game. The only thing that privileges constitutional rights over statutory ones is that constitutional ones are harder to repeal.

So, if an amendment actually restricts the free speech protected by the first amendment, which one takes precedent?

The newer amendment trumps the older one. Always. Else we’d still be debating whether alcohol is illegal, on the theory that the 21st Amendment unconstitutionally violates the 18th.