I've never observed puakeninkeni to be seasonal- just keep cutting off the fruit every month or two, before it develops very much, and you should have flowers all year round

What if it's already 5' tall and never flowered?

We have such a pua kenikeni that has never flowered, purchased on Maui. One of the cuttings of the original plant is about seven feet tall now. We often wondered if it really is a Fagraea but a botanist who visited us took a look and thought it definitely is one. Looks like it might do well as a foliage houseplant with large green succulent leaves.