I had the exact same problem as you with the exact same symptoms on a 1996 XP 800 I was just working on. Ski ran great on my driveway then the owner took it out and after about a minute of riding it would not start and he tried new plugs and nothing but it tried one or two times. I got it back and the spark plugs were wet but had good spark and compression. I turned the fuel off and grounded the plug wires and when I cranked it with the plugs out lots of fuel shot out of the spark plug holes. BINGO! Flooded big time. I cranked it a few times with paper towels over the holes and throttle wide open to clear the fuel. I cleaned the plugs with brake cleaner and hooked everything back up but kept the fuel off. It fired and puked all kinds of black goo and fuel all over my driveway. I then turned the fuel back on and it ran fine but.... With pressure in the tank I could hear fuel running so I pulled off the air cleaner and with a mirror I could see fuel dripping from the bomb sight in the rear carb. When I pulled the carbs apart again there was a small piece of plastic like a tooth brush bristle in the needle and seat keeping it from closing.
I would bet you have leaking needle and seats. Blow some pressure into the fuel tank throught the check valve where your hood closes with your mouth and take the air cleaner off so you can see into the carbs with the fuel on and a mirror I bet you are going to see fuel leaking, drip, drip, drip into the carbs.