I have a bushy flame tree that has lots of branches off the base. Can I prune it so it has 1 main trunk? We are in the desert.
Absolutely! This is a good way to keep it shapely, and nice looking. Here is an article that will help you with the care of the tree:
https://www.gardeningknowhow.com/ornamental/trees/flame-tree/flamboyant-flame-tree-info.htm
ed by 30deg . Will they come back?
Make sure to cut back any dead foliage once the threat of cold weather has gone. When you do so, you can do the "scratch test".
https://www.gardeningknowhow.com/ornamental/trees/tgen/tree-scratch-test.htm
If the shrub is still alive, then you can begin to care for it until it returns to a healthy state.
https://www.gardeningknowhow.com/ornamental/trees/flame-tree/flamboyant-flame-tree-info.htm