I am no expert on this tree, but will ask some questions, which if you answer might help others who might be better able to address your issue, and who know more about this type of tree and your location.

This tree needs medium moisture, but if well established has been reported to be slightly drought tollerant. It also is only intermediatly tollerant of shade.

Since the tree has survived for 7 years, that must indicate that the bottle palms are not taking away too much of your tree's available soil moisture.

Do the Bottle palms shade your tree at any point in the day? If so that could be contributing to your tree's inability to bloom.

Other wise, consider that every once in a while reports have shown up on the web, from some person or other, commenting that some Delonix regia trees can take up to from 7-9 years before beginning to fruit.

One other thing to check is the ph levels in the soil where your tree is planted. Is any contributing factor near the tree which could cause the soil where the tree is growing to be out of the Delonix regia's preferable 4.0-7.0 ph range.

Also double check that the area, where the tree is planted, does not have a lot of coarse textured soil. If so, there might be just enough there to stress the tree and cause it not to fruit, but not enough to keep if from surviving