The First Amendment doesn't allow anything. Like the rest of the Bill of Rights (including the Second Amendment), it guarantees government cannot interfere with rights that preexist government.
But yes, that would be a protected publication. He never challenged it. The designs were already out there (so he won), and it would have been expensive. I believe they used the same ITAR crap that used to prevent us from exporting encryption. But the courts ruled there that printed copies of encryption algorithms are protected expression, so this should be as well. More importantly, the Constitution does not grant the federal government any authority over publishing firearms plans.
And finally, when have you ever known the federal government to abide by the Constitution?