NRA's Chicago brief
Pdf is here. Between this and Petitioner's brief, I think the ground is covered very well. Petitioner emphasizes incorporation under the privileges or immunities clause (which makes far more sense) and NRA emphasizes incorporation under the due process clause (which is simpler to do).
NRA files, not as an amicus, but as respondent in support of petitioner. In case you wonder what that is -- NRA also filed an appeal (a petition for cert.), but the Supreme Court took the SAF case and not the NRA one, which remains pending. The Clerk ruled that NRA, being a party to the other appeal, was entitled to file as if it were a party (meaning a longer brief, but deadline yesterday). It'd obviously be in support of the Petitioner. But custom is that anyone not a petitioner and not an amicus is a respondent. So they wound up as Respondent in Support of Petitioner).