Please Help Me!!!!!

I just got a 1991 zx6, It ran great when I got it. I did the usual change oil, plugs, fuel filter, oil filter, drain the gas, new air filter, after all that I started it up and it ran great, then as it warmed up it started backfiring and died, wouldnt start, 10 min, later started right up, as it warmed up same thing any help please.......could it be a vent problem thats what my local dealer told me, how do I check it? Help me please thank you in advance....

the carbs could be clogged up, perhaps one or two cylinders aren't firing. check the ignition system, like the primary coil, check the bolt and connectors. check the starter and the battery. I've had similar problems.

take off the fuel tank cover and airbox to see if the intake boots or hoses connected properly to the airbox or if there's any leak, although I don't think that's the problem, but this way you can check out the carbs and ignition coil. check to see if the carbs are flooded or (choke cables??) is connected properly, sometimes too much choke will also flood the carbs. take out the plugs (new??) again to check if there's already carbon deposits on it already or not, that could mean one of the carbs is running to rich. so check to see if the bike is running reach, the way you can tell is if you rev it hard above 8K, exhaust would let out black smoke and sometimes even unburned gas.

sometimes undajusted carbs or jetkit would also make it run rich.

if those are fine, you can check to see if there's any electrical problem with an ohmmeter or something, check the regulator/rectifier, fuses that connect to the battery, or alternator if it gets worse (though unlikely).