Drop bar levers work poorly on flat bars. Ignoring the difference in diameter, they really need to sit on the crest of an outside curve.
one thing that MIGHT work for you is to use a North Road/Mustache bar. These provide an outside curve where drop bar levers might be mounted.
The levers will sit flat and you may not be happy with the ergonomics.
I’tll be cheaper than finding flat bar controls though.