Legally: Yes it makes a difference, you can be of full age in one country, fly to another and not be of full age. However, this will rarely be the case. And it is reversal. Let's say you fly from A to B and you are 10 hours older, because in B it is 10 hours later, and you fly from B to A again you get 10 hours "younger" - from a legal point of view. So you cannot really accumulate it, +1 day is the maximum (you need to fly over the international date line).
More a curious point: When you fly, you will get old slower than the people on the earth who do not fly. This is the natural sciences point of view, based on the special relativity and we talk about differences of parts of a second. Please see this Wikipedia article if you are interested in a more detailed version. However, it is true. I remember an experiment where they flew with an atomic clock (most precise clock in the world) and afterwards there was a small time difference between the atomic clock which flew and the ones which stayed on the surface of the earth.