All what Reece said, plus:
Do not stop when escaping from the destroyer(s). Simply click on the speed indicator and reduce the speed to ~2knots. Your engines will be harder to perceive and at least you will have a momentum when the time comes for a brief getaway at flank speed.
However, remember to go at flank speed only to escape the ships that you think is going to drop the depth charges on you. In addition, when the ships are moving away, they cannot ear you. So move fast when they move away, and move very slowly when they are closing on you.
Anyway, you will get the drift soon; you will learn their ranges and angles in which they operate and flee between them like if nothing happened!
And welcome to subsim