I currently have a Tech One foamy that uses 2 cell 7.4 lipo 800 mAh. I can get about 6-7 minutes depending on how aggressive I fly. I was wondering if I could use a 3 cell 11.1 1000mAh? (I have a bunch of them) Will the 10A ESC handle the additional amperage and will the T-Motor AS2204 KV1700 also handle the amps? If I can use the 3 cell will I get more flight time and a little more power? (I say yes despite the increase in weight)

You will have to look up the motor specs and see if it is rated at 11.1V. Now the bad news, you will get more performance but I would expect the same flight duration. Adding an additional cell slightly increases the battery's internal resistance. The motor will pull more current at the higher rpm unless you drop down in prop size. You will also need to use more throttle with the increase in weight. Think of it like adding a supercharger to your car. It increases efficiency but adds power in the process. It requires fuel to produce power, in this case it is amps.

Voltage is the critical issue here what is the voltage of the 3 cell fully charged? If the system is not capable of handling that voltage you'll burn things out

Get bigger mah 2 cell batteries. that will increase your flight time

Increasing the voltage will increase current draw = shorter flight times. No free lunch in electronics. Agree with above. If you want longer flight time, get a larger capacity 2-cell pack. Your ESC\motor may not accept 11.1v without burning up.

I did it and got less time and less performance. It just got kind of heavy.