Seems like my 1999 300 Honda fourtrax isn't getting enough gas

Check the screen at the bottom of the petcock (fuel on/off valve) it could be plugged up with crap and cutting off fuel flow. You can remove the bottom bowl of the valve and the screen and a plastic clip will come out. Mine was very full of rust as well as my tank, I put some screws in the tank and shook it till my arms hurt then spent the next two hours fishing out the screws, cleaned the valve and the carb and added an inline fuel filter in the process to keep that junk out of the carb.

If you have a carb kit in it and sure its clean and your air filter is good try running it with the air box lid removed see if that makes a difference, however if your plug is BLACK that does mean its rich which means too much gas so maybe the float is out of adjustment, or has a hole in it or is sticking?

I assume the carb kit came with a new main jet. Did you make sure its the right size? It should be either a 120 or 125 main jet.