I like the concept, it just doesn't quite feel finished / polished. I like the idea of the arrow appearing in the in the flames yet almost blending in with the flame. Great idea.
If this could be polished, this could be a winner. Notice how in #42 the arrow is created by virtue of the flames. Whereas in #44, it looks like you obviously cut an arrow out of a ball of fire? I would like to see a logo where there are flames, and from the flames and the pattern within the flames, you can see an arrow.
#55 is getting closer to the idea, so you are grasping the concept, but it is not a very clean and professional looking logo. Try to imagine that on a shirt or mug as well as on letter head and the website. It would be difficult to design around. But you have the right idea. Now if you can simplify it.