Have you looked at the Alaska website for mileage seats on Emirates in February? I would first see if you can find two seats on the same plane in F - probably not. You do this just by searching for your route and ticking miles only on the first page. You may also need to get to Dubai and then see if there are seats from Dubai to wherever and put the two together by calling the Alaska desk.

If you buy miles, just go on the Alaska website, sign in to the Mileage Plan page and click on buy miles. You'll discover it's about $29 when you include the taxes per 1000 miles so you would spend about $3600 for those miles. For what it's worth you can usually call the BA partner desk, see if the flights are available and ask them to hold your seats if they are while you go and buy the miles and then call them back. You would do better to postpone this trip and buy miles when there is a promotion - it can be as much as a 50% bonus so you would buy about 80000 and get 120000...give or take.