I had to choose between jogging with a bra, and giving up jogging. I (temporarily) gave up jogging.
I just couldn't face exercising without a binder, and wearing a binder restricts my breathing to levels that would be dangerous if I were jogging. I tried it once and I felt very light-headed and dizzy. That's not good for an asthmatic like myself. So no, I wouldn't recommend jogging with a binder.
As an alternative, I use the recumbent bikes at the gym to do a 'long, slow burn', i.e. an hour-long session whilst making sure my heart rate doesn't go above 65% of maximum. I can do that safely whilst binding with a relatively loose binder.