I have a 98 zx6r that when I start it. It starts right up runs for a few seconds then dies. If I pull the carbs apart and put them back on it starts right up. But I leave it over night It won't start. Once it fails to start it will start backfiring. Hopefully someone has an idea where to go with this

 

check the float needles during the carb rebuild/cleaning. You did not mention if you were using the choke either. Welcome to KF

 

^^^ this.

you could be upsetting the floats enough to allow gas to fil lthe bowls initially. then when they seat to shut gas off, the gas gets used but the floats don't drop.

try various cleaners.. if theres no avail, then go thru the carbs carefully.