Doe anyone actually know how to fight with a tomahawk?

There are some problems I see with the "fighting tomahawk." It is heavy, and thus slow. It is certainly heavier and slower than a machete/bolo/short sword, which has about the same reach as it does. Even though axes have more chopping power, it only shines if you need to get through armor. A machete is powerful enough to kill. Second, the geometry is tricky. You'd need to know how to grappling with it. Close up, someone can easily grab the haft, whereas you can't grab a machete. So that means you need to know how to fight somebody grabbing on to your tomahawk. The shape of the axe means you can hook with it, but that also means (1) you need to know techniques to make that feature count, and (2) your tomahawk could get caught on something if the chop is not successful. Finally, the tomahawk is not a thrusting weapon. That's a disadvantage when grappling. It's hard to slash or chop when close up. (On the other hand, I wonder, with the mass and geometry, perhaps you can sink the axe into flesh more easily just with the wrist.)

How about throwing the tomahawk? Bad guys who are worth their salt band together. After you discard your primary weapon by throwing it against the first bad guy, what will you use against the other two bad guys? How many tomahawks do you plan to carry?

If I had to choose a weapon, I'd probably not take the tomahawk, no matter how black and "tactical" it is. But that may just be because I never studied the tomahawk. People did use axes for fighting in the Middle Ages, but the fact that Vikings could do it doesn't mean that we can do it also.