I run a 4S 6000 mAh lipo. The F550 handles it easyily. I also run that same Lipo on my F550 conversion. With the larger AXI 2814 motors, and 12" Props, I am getting 15.36 min flight time (Battery voltage at end 14.9v).
Yes that was with the Conversion. No Landing gear or gimbal. The 6000 mAh is the Nano tech 6000 4s. I also tested the 8000mAh Zippy 4S and got 16.47min (battery voltage at end 14.9v)
UPDATE: Stock F550 with 8" Props
I just did 3 flights using a 4S 6000mAh lipo. I was tuning and testing a build I just finished for a customer. 3 Flights all resulted in 16-17min flight times. That was using the 4S 6000mAh lipo, with stock DJI 8" props. I am pretty stoked to see that the conversion kit gets pretty dang close to the stock flight times.