Can I convert a 11.1V 2200mAh 25C Li-Poly Battery Pack Deans with Deans Female to Small Tamiya Female to work with a stock M249 or with this burnout my motor?
You can build an adapter for practically anything. Whether the motor burns out depends on the battery you use, not the connector. They are two separate issues. If the motor is going to be burned out by the 11.1V 2200mAh 25C Li-Poly Battery Pack, then it will get burned out whether you use Deans or Tamiya connector. Having said that, the question is whether the Tamiya will be able to handle the current that the motor draws (without heating up and melting. That depends on a lot of factors, such as how much current the motor will draw, what kind of wires you are using, what kind of gears you are using, etc. Sometimes, that just requires trial and error.