Legal Question in Constitutional Law in Vermont

The Dick Act, which is also called the Militia Act of 1903 (the name you cite is not correct), dealt with the structure of the National Guard. It did not invalidate gun-control laws.

The Act is just legislation and not a constitutional amendment. In the federal government, legislation cannot forbid other legislation in the future. If a law is passed today that contradicts a law passed years ago, then the new law prevails. Only a constitutional amendment -- or a Supreme Court opinion interpreting the existing text of the Constitution -- could bar particular types of future legislation.

Federal legislation does trump contrary state laws, so if Congress and the President ever forbid gun-control laws at the state level then those laws will have to yield. (It's possible that such a federal law would be unconstitutional, but that would depend upon precisely what it says.)