How can I add flavor to green tea at home?
Depends on the flavour I suppose. For the most direct route, I would try just steeping the fruit/flavour in the tea/water for a bit (ie: sliced strawberry, sliced ginger, lemon zest/peel, etc...). I make a ginger/lemon "tea" with thin slices of lemon zest by just steeping it in water. No reason you couldn't add some green tea leaves to that as well. Lemon Juice, I add before serving.

As mentioned finding an extract could work as well. No idea about amounts, you'll have to do some research as to what is safe/appropriate. I haven't used them.

For a Jasmine Tea, I would probably just find a good tea purveyor and find a proper Jasmine Tea.