It's likely your AS number isn't on your booking. You can sometimes fix that on the BA site or app, but I've had better luck going to finnair.com and doing it there (just enter your BA confirmation code under "manage my booking." Look for where you can enter your frequent traveler number, select Alaska and enter your number). Once done, that may let you select seats on the Finnair site, but if not, give it about 10 minutes, and then you should be able to go back to ba.com / manage my booking and select seats.