15 minutes is a long time ! Do you ride it for 15 minutes and then it stops? If so I would be surprised to hear that it runs for so long.
After it stops does it fire staight back up?
I would check the following,
Is the fuel filter full of crap?
When it stops are the spark plugs wet, if yes then you've probably got an electrical failure.
Is the breather from your fuel tank blocked so are you causing a vacuum in the fuel tank after a while?
Have you checked to make shure your choke is off? If you have a cable choke make shure it is realasing. Somthing else most people forget is to lube the carbs cross shaft, somtimes the choke enrichener (plastic cam) can bind causing it to think the choke is still on making the carbs run rich. Just my 2 cents as 15min is normal warm up time.
Okay that helps with Flatslides and wet plugs you probably have a sticking float. That is why if starts to flood whin idleing or at low speeds. at high rpm you are using the extra fuel. At lower rpms the floats fill and then overflow flooding the motor. Has is been sitting for a while? If so I would try leaving the petcock on with the bike off and see if fuel begins to leak out of the overflow vents. If so your floats are sticking and need cleaning/adjustment. If not you may have another trouble.