No! That for sure doesn't look like a flame tree as you can see that the tips are kind of pointy, it looks like a blue jacaranda (I'm growing a few of these from seeds myself, although they're from my backyard). You should not keep them in a warm climate! Keep them cool until they're about 1.5 years old. What hardiness zone are you in? They best grow in the SoCal-Arizona side in the US. (Though you may not be in the US.) The hardiness zone they thrive in is around 9a-9b. (Which is where I live) You should stop watering them on a schedule, water right when the soil feels slightly moist. It looks like the leaves are drying and getting fried, keep a humidifier next to it to prevent leaf drying. (though it is not enough to do that) Give it a thorough watering now (Like right now, when you read this message) because it is probably already half dead. Do the bark scratch test, where you remove a layer of the bark to check the colour:
If it's green, it's alive.
If it's brown, probably dead.
These trees are semi-deciduous, in other words, they lose their leaves for a very short period of time in the winter. Not during this time. One time, I took a cutting off of the Jacaranda tree in my backyard, but it's leaves fell off after a few days. (Because of lack of water.)
Long story short: This tree is a jacaranda, these are semi-deciduous. The leaves have dried up, give it a thorough watering, NOW.
I hope that this helps, sorry for the long answer!
