YZF 250 has a hard time starting but when it's warmed up it runs great. Usually only starts when you are rolling down a hill. Kick staring is near impossible.

Always first of all you need to look at the condition of the edges of the intake valves. It is likely that they are the problem

Check the heat range on your plugs or their general condition. Wouldn't hurt to run a carb cleaner and do a general tune up as well. Hard to start when warm is usually a fouling issue with the plugs or a fuel air mixture problem.

Normal routine maintenance can fix the problem most of the time.

Valve adjustment and timing likely targets here. Had a 250 L with same symptoms, found timing/valves the cause.

My guess would be you had water in the fuel. going up the hill put the water in the floatbowls right in the pickups for the carbs and going down pulled the water away.

Not sure of the age of your YZ 250 ( You never said!) but in most Yamaha they use dual stage stator which means a stator will charge a spark plug at two speeds one on kick starter speed and the other on running speeds it is common that the low speed circuit on the stator to fail leaving you with a bike that only starts when pushed its a very simple test to diagnose it be worth checking you have spark on kick starter speeds with spark plug out the motor but still connected

A shft is broke or bent bad or a bearing got real hot and welded itself to the shaft. If you can roll down a hill and put it in gear and jump it off its one of the two prior problems. it it want start the motor might be seized up.

check your intake and exaut vavles that was my problem

If they where to tight it would not start when cold, and get easier when warm. I would look at overheating check oil/coolant levels.

i got a 2000 rm 250 and it used to be a cow to kick over i used to spend at least 20 min kicking to start it until i rebuilt the top end with a new piston and rings now it starts on the fourth or fifth kick if that doesnt help you need a new cpu good luck!!!!

needle and seat are worn out in carb, to much fuel is flooding cylinder. remove carb, clean, get new needle and seat, set float. problem goes away. pull your plug after kicking. its probably wet.
When you push, or pull start you evacuate excessive fuel, when engine is warm, easier to start extra fuel burns easier.