If I put the choke on I can get it to 6000rpm but that is as far as it will go. The whole top end has been rebuilt. This problem exsisted before I rebuilt it. New pionts, plugs, rings and all gaskets. I had the same problem with my cb200t and I cleaned out the main jets and that fixed it but on this 350f it has all new parts in the carbs. I put a inline fuel filter on it before I started it up.
Like Bender says, lose that filter. There's not enough hydrostatic head on these small tanks to support the filter's pressure drop, so the float bowls will drop low when running over 1/2 throttle. Make sure the fuel lines leave the tank and run as horizontally as possible enroute to the carbs, then go vertically the last short bit into the carb's nipples. It's not simple here, but the routing is pretty important.
Next: sooty plugs indicate over-rich mix. 3/4 turn idle screw leans out the mix: this verifies it.
The most likely problem: the tiny air passage from the air horn into the top of the emulsifier tube is blocked or partially blocked from collected grains of dirt, corrosion, and dried fuel from sitting. This tiny passage (in each carb) has caused more problems like the one you're describing than any other single item in these carbs, from the Twins to the Fours. It's not easy to clean, and soaking and blowing will not clean it. Running a small wire through each one carefully, back and forth, with the emulsifier tubes removed, is the only way to loosen the crud: blasting through with carb or brake cleaner must be next, repeat as necessary.
As an example: after my 750 sat 5 years while I had cancer, all 4 of these were 50% or more blocked. The symptoms resembled yours, but at 750-like speeds (80 MPH tops, where it normally is 130 MPH top end). I took them apart 5 times and cleaned them before I finally got them all cleaned.