Yes, you can fly to Berlin on Air Berlin for $17 plus Avios, but that is from LAX, not SEA. The BA website will not let you book Air Berlin from SEA because they do not serve this airport. Maybe you could get it by calling, but I don't know. Plan on a 30-minute wait if you call.
But if you want to go to the UK, why fly to LAX and Berlin on the way? To fly direct from Seattle to London on Avios, I suggest you fly Business class, which is a much better use of Avios than Economy. It will cost you around $900 RT but is well worth it. We do it once or twice a year. Book one way at a time, 355 days in advance.
We have also used Avios to fly Qantas from Australia to LAX in Business class. That could be booked online. I have also heard of people using Avios for domestic US flights on Alaska airlines----do you have any wish to see Alaska? You have to call to get that one too.
Flyertalk forums can be very helpful with this kind of question.