There used to be a few flight schools around Dubai before 2008, but they all closed in the meantime. Now as far as I know there is only three schools left, all of them aimed at professional training: one in
Sharjah, one in
Fujairah and one in
Al Ain. I don't think they do rentals, so best case scenario you would have to be flown around by an instructor, but not even sure that is possible anymore.
If you are interested in microlight, there is a club at Al Jazirah (Al Jazirah Aviation Club), but they are very limited in terms of available airspace: I don't think you can fly higher than a few '000ft nor further than a few nmiles away from the airport.
Happy to be corrected though so let me know what you find...