"Can anyone tell me about the Illawarra Flame Tree? When does it flower? When does it loose it's leaves?"

Have you tried googling this? Much information (including bloom period, etc) is available with just a quick search. Is there something in particular you are looking for that you haven't been able to find?

"Would they be ok to have beside a pool for shade?"

Well, it wouldn't be the first thing I'd think of as a pool-side tree (grows fairly large, has considerable litter, etc), but I guess it really depends on whether you are willing to clean up after it and whether you want a large tree near your pool.