No fee if the AA segment is first and everything is one ticket.
If booking round trip, AS will charge a fee for the return. However, bags on flights entirely within Alaska are free. So if you fly FAI-ANC-DFW, with segment 1 on AS and 2 on AA, there’s no charge.
Free bags for AA elites on all AS flights will start in summer 2021, assuming AS follows through on joining OW.
You can also get the Bank of America Alaska Visa card that offers 1 free bag per person (plus other perks).
Click here for BofA info