Alaska Airlines--which alliance
 

Any ideas on which alliance (if any) AS will join? I've been looking at their website and they have alliances with the following:

Skyteam X5: Air France, KLM, Continental, Delta, Northwest
Oneworld X5: American, British, Cathay, LAN, QANTAS

I doubt they will join any alliance. They seem quite happy code sharing with everybody.

What would the advantage be?

I would be rather surprised if AS formally joined any alliance as well. They have very effectively played "Switzerland" - gaining partner revenue and mileage redemption opportunities that exceed the major alliances. I rather doubt joining one of the majors would outweigh the resulting losses.

About the only thing you might expect AS to do is grab some continued 'goodies' as convenient. (e.g. the limited upgrade reciprocity with NW or the full club reciprocity they have with CO and NW).

I heard that you can get elite qualification miles on FB when flying AS, but the website is not very clear...has anyone had any experience with that?

You used to... in the good old days of Flying Dutchman when every mile was qualifying... Not any more, you definitely don't