I work on the fire/rescue side of things in my area, but we do have a subject who just got through his fire and EMS training who wears HAs. He is HoH, but is able to hear what people are saying and understand it without reading lips, etc. He is able to do anything in the field - he even drives the ambulance. As far as a deaf firefighter, I am not sure (or police for that matter). The biggest issue I can think of is that the majority of communication on a fireground, or responding to an incident, is done over portable radio system... If you can't hear that, it would make it hard to coordinate things you may need to know (ex. an emergency evacuation of a collapsing building on fire). You may be able to be a field officer, but on a 2 person crew (2 to a car). There are many other positions in the LE field and even on the fire side that you could easily get in - logistics, detective work, processing, etc...
I work in the city again tomorrow - I am going to talk to some folks and see what I can find out about requirements and such. Not sure that the topic of a deaf officer has come up in the area (as surprising as that may be). I will get back to those who are interested in an answer.