Gluten-free flours can be stored in the refrigerator for 3 to 4 months or in the freezer for many months.  Just be sure to bring them to room temperature before cooking with them.

As for storing finished products, I have my best luck freezing most as the refrigerator tends
to dry them out and make them brittle.  (Think leftover rice from the Chinese restaurant.)  Most baked goods can be wrapped and left on the counter for a couple of days to enjoy fresh.  Then wrap remaining baked goods in portion sizes in plastic wrap and place several in a zip lock bag before freezing.  To revive, wrap a portion in moist paper towel and microwave for 30 to 60 seconds or just until slightly warm.  Then toast, bake or eat as is.

The exceptions are cream and pudding based pies, cheesecakes, and anything with fresh fruit in the center or on the topping.  Fruits baked into pies will freeze well.