So you'd be getting two cats on the very extreme ends of the behavioral spectrum (in terms of breed stereotypes at least). One boisterous, athletic, with a high prey drive and a need to have frequent physical stimulation. The other affection-seeking, docile, friendly, cuddily.
It's difficult to predict how things will turn out because all cats react differently, and you might end up with a cuddily, sedate bengal and a prey-driven maniac of a birman. You just don't know. But playing the percentages, chances are your bengal is going to rough-house and chase your birman all over the house, and the birman is going to just want to escape this fur-devil and be left alone to his warm window sill (or whatever). Note that, in general, kittens are going to get along better than adult cats. So getting two kittens about the same age, at the same time, increases your chances that they will at least temporarily accept one another (but when they get older that may be a different story).
So you should plan for that. What's really important is to provide vertical spaces so that, for example, your bengal cat select "his" cat tree or wall shelving, or window sill, and the birman can select a different one, not adjacent to the bengal (in opposite sides of the room, or in different rooms). Allowing the birman to have "safe havens" off the ground also much more easily defensible positions, which may reduce the drama and stress that the two cats feel. Also, similarly, once you start to see any sign of the birman being terrorized or stressed out by the bengal, you will need to make sure you provide litterboxes and food bowls that are also spaced apart.
So right off the bat I'd get either wall shelving, or cat trees or both.
http://www.catsplay.com/cat-wall-climbing-systemsFor cat trees, the higher the better (especially for the bengal). Don't bother with anything less than 5' or 6' high imo.
https://www.amazon.com/Armarkat-Pet-Pro ... B003BYQ18M