Kx250f

First of all..Welcome! Second...When you kick the bike over, are you "feeling" the same compression/resistance as when you were kicking the bike before this problem occurred? Does it bump start easy? and everytime? Any power loss while riding?

A buddy of mine had this same problem with his KX250f, and his problem was that his valves were in spec, but his exhaust valve was worn out. Bump starting it worked because when you bump start a bike, the motor turns faster than when you kick it, making it easier for the bike to start. Here are a couple other things i can think of that could be the culprit, none of which i have experience with..just guessing, maybe a good place to start.

Timing may be off.
CDI issue?
Coil going bad?
I believe there is some sort of flywheel sensor that can go bad?
Auto-Decompression not working.
Neutral switch not working, (if your bike doesnt usually start in gear)
Have you had your kickstart shaft or spring out?

Spark, Fuel, Compression. 1st Remove the spark plug and reinstall the plug into the cap and turn the engine over checkimg for spark. 2nd check the pilot jet (sometimes called slow speed jet) for blockage, make sure you can hold it up and look thru it like a telescope and see thru it cleanly and clearly. 3rd Check for compression with a compression guage (old school remove plug and hold finger over the plug hold when compression stroke it should have enough pressure to push finger off plug hole). I know you said you check valve clearence but low compression ( valves too tight or woren rings) can cause this also.

Recheck valve clearance.

Recheck valve clearance. ( i will second that option..) __Sounds like a leaking valve..