I have an African Gray and he does the same thing. I have been told that he is exercising. My bird has his wings clipped ans cannot fly aoI guess he is getting practice so when he can fly he will be ready. Mine is almost 2 years old and he stared doing this about 2 or 3 months ago.

 I had the same problem but it's the female which did this. Being in a small cage, budgies have no room to fly and exercise their muscles so they flap their wings in order to keep healthy but it's not enough. You should probably get a larger cage as they seem uncomfortable in the one they are in.