the alarm system flashes the flashers and prevents starting when activated. try unlocking the doors with the key in the lock to "reset" the alarm. usually the alarm horn would have gone on at first then timed out to just the flashers.
If this was just a problem with the hazard lights, I'd say check the switch, but if the car is cutting out at the same time, you have a bigger issue. This is an electrical issue that needs the attention of a qualified technician that has the experience and equipment to diagnose this type of problem. I would take it to the dealer or a high end European shop, tell them what is happening and try to duplicate the problem for them. They may have seen this before, but that won't be the case with an in-experienced Audi shop/technician.