Klx250sf starting with choke on but dying when given throttle or taking choke off
 

You likely need to clean the carb. Sounds like the pilot jet is clogged...and the main could certainly be as well.

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You may want to have a spare pilot jet on hand when you get into the carb. They are fairly inexpensive and difficult to properly clean such a small orifice.

It may also be clogged in the fuel passage, which may require either a carb washer or ultrasonic cleaner bath at some car or bike shop. They work the cleaner into the passages you cannot get into.

Pilot metering circuit is still clogged. You will need to follow klx's advice and use an ultrasonic cleaner to resolve the issue.

I've used the old pinesol soak trick, many times on gummed up old carbs with great success. I've never had any issues but I have seen some people say they have destroyed old rubber seals etc doing that, so do so at your own risk.

Many automobile shops and motorcycle shops have carb washing or ultrasonic cleaning machines that work cleaner up into places and vibrate loose or work to dissolve dirt, crud and gummy old dried out gas residue. Take the body in minus jets and other easily removable jetting bits, don't worry about butterfly and linkage, also take in the float bowl just because. Shouldn't cost much since they will have no labor in it other than putting it in, taking it out, rinsing it off and handing it back to you.

Maybe turn the idle screw up a bit.