What are the qualifications for Expert Field Medical Badge (EFMB)? Can I request this training after going to BOLC training?

You'll more than likely have to wait until you get to your unit. They have a team that travels around offering the qualification course. As far as the training, you'll do the train up with your unit. The EFMB Qual itself is the culmination of your unit level training. Pass and you get the badge. It's a difficult Qual though. Hope this helps.

I would expect that you will have to request for this once you get to your first unit. But that's also a good thing, because often there is a unit-level or base-level trainup that you can go through. In the case of EFMB, that can really help. Plus, you would be going through this trainup with some peers from your unit (brigade, etc.) and that's a good way to build some relationships. Anyway, there are exceptions to most things, but in this case I would plan on trying to request this when you get to your unit.