Is Blackheath a fire prone area?

Yes it is fire prone and you will always have to live with that. Try to look at the council maps for a list of the non fire prone streets. Im not sure that there would be many in Blackheath but South Katoomba is better.

All of the Blue Mountains is fire prone. That is one of the things about living within a World Heritage National Park. Having said that many of the residential streets closer to town in Blackheath have no fire risk rating. If you go to the BMCC - Council web-site you can search individual houses and see their fire rating. http://www.bmcc.nsw.gov.au/bmccmap/parcel_search.cfm

Yes, Summer is always a tense time in Blackheath and the Mountains generally because of the threat of fires. We are surrounded by Blue Mountains National Park and there is one main road in and out of Blackheath.
The Rural Fire Service is great and keeps everyone informed with doorknocking and town meetings at the beginning of the season.
If you want to have the beauty of the park then fires are just the risk that you accept.