You can make grips out of any kind of wood. Burl wood grain is not linear or cross-linked, and it is comparatively soft and fragile. No problem, though, it is easy to reinforce burl wood or any kind of wood with an epoxy overlay. If you look at many commercial burl wood grips, they often have a very thin fiber backing that is epoxied in place. That is there to add strength. But many types of wood can be used satisfactorily, there is not much load on the grips. They are just something to hold on to, the frame of the pistol takes most of the stress.
Good wood for grips will be hard, fine grained, dense, and able to take the wear and tear they will encounter. Pretty to look at is an added bonus. There are way too many types of wood suitable for grips for me to list, but think of the "usual suspects" like ash, hickory, walnut, bocote, bubinga, cocobolo, ebony, pau ferro/ironwood, mesquite, maple, just about any fruit wood (apple, quince, plum, cherry are commonly used), rosewood, zebra wood, etc, etc, etc. And there are some very attractive laminates and dyed woods these days as well.