What is the flap in throat behind your tounge that you can feel if you stick your finger in your throat?

Epiglottis. Actually, you're probably feeling your epiglottis, which is a structure that protects your airway when you swallow. My best advice is to stop sticking your finger down your throat!
Uvula. I believe you are referring to that little hangy down thingy! it is called the uvula. Don't know the significance except that it always gets infected, swells up and causes a lot of people to ask this question.