Your tire might the the culprit. Feel along the inside of the tire for abrasions or holes. Feel along the side wall of the rim. Lastly take note of where the holes are on the inner tube. You got 2 ways of doing it. pumping up the tube and putting it in a bucket and searching for bubbles, mark area with tape or with white out. You can also pump up the tube and just feel for air coming out. The first works good on tiny holes, and the second doesn't work so well with tiny holes. You could be pinching tubes as you replace them.
So once you figure out how you are getting the flats fixing the cause is easier.
