DIAGNOSIS The dust blower on the DCS570B is just a simple channel that directs air from the motor fan. It's not a separate part. If it's clogged, you get no air.
FIX The exit port is right in front of the blade guard. It's a small hole. Get a thin stiff wire (a paperclip works) and carefully poke it into the hole to clear any packed sawdust. Then, use compressed air to blow backwards through the exit port and also into the intake vents on the motor housing. Do this with the battery out.
IF THAT DIDN'T WORK If the airway is clear but you still get no air, the motor fan itself might be damaged or obstructed. This requires disassembly to inspect the fan blade on the motor shaft, which is a more involved repair.
HEADS UP This happens a lot when cutting MDF or really resinous wood that creates fine, sticky dust. Make clearing that port part of your post-job cleanup routine.