I've never seen them together. The yellow spiny eels I had, which are alot like the tire track eels from what I've seen, always burrowed under the gravel with just their heads sticking out. All the fire eels I've seen have always been hiding in caves or wrapped around rocks. So when it comes to where they hang out I don't think there would be much of a problem.
But don't fire eels get a lot bigger, thicker and longer, than tire track eels? If so you never know what's going to happen, some day you could find part of the tire track sticking out of the fire eel's mouth.
If I was to venture a guess, I'd think that the fire eel, because of size differential, would kill the tire track eel. But anything is worth a shot once.