Kacey & Rajesh,
Many trees are called flame trees.
I think Kacey that you referred to Delonix regia, which IMHO is the "real" flame tree. But There is also a blue flame tree (Jacaranda mimosifolia) (which is Zone 9, Rajesh) a yellow flame tree (Peltophorum pterocarpum, which is zone 10), dwarf flame trees or dwarf poincianas (Caesalpinia pulcherrima, zone 9 and Caesalpinia giliesii, zone 8).
Rajesh, reading this forum, I understood you live in a USDA zone 9b equivalent climate, or so. For you needs, I think you definitely should have a closer look at Jacarandas and Caesalpinias, these plants are worth investigating!
MariaSan Francisco Bay Area 