No, snakeheads and bichirs are not related at all. Bichirs (family Polypteridae) are a much more primitive fish than snakeheads (Channidae). Although this is a gross oversimplification, they (bichirs) are placed somewhere between the lungfish and the gars and bowfins on the evolutionary ladder. Snakeheads are more closely related to the gouramis, climbing perch and Ctenopomas.
While both genera breath air, the organs used to do so are completely different. Snakeheads have a labyrinth organ in their gill chamber that is similar to the one found in gouramis and the like. Bichirs have a paired swimbladder that functions like a primitive set of lungs.
The similarity in form you see is the result of a phenomenon called Convergent Evolution. This is when completely unrelated species (often on different continents) have evolved similar morphology to take advantage of similar niches (a niche is basically a combination of habitat and lifestyle).
Both bichirs and snakeheads are predatory fish that inhabit oxygen poor waters and can survive periods of drought by burying in mud or moving to other pools, etc. Their methods of hunting and prey capture are very similar to each other, they are torpedo shaped with a broad, powerful tail for quick attacks, but they are completely unrelated. Interestingly, the bowfin (Amia calva), which is also completely unrelated, fills a similar niche here in North America (you could almost call them the American snakehead).
