Hi, JT!
Oh, and Mike,
JT's advice is good, I won't repeat his answers.
See if you can find some bougainvillea fertilizer, called Bougain. You want a ratio of 1-2-3, rather than 10-10-10, or 'bloom booster at 15-35-15 or whatever. Adeniums don't need much nitrogen, makes them just grow leaves.
The pot looks rather deep, is the white part painted or baked on? Not good, the roots and mix can't breathe through that. Find a shorter, wider pot. If you dislike plain clay pots, put it in a roomy pretty container.
And start cutting way back on watering for the rest of fall/winter., as you might know. These plants can be bare root, out of any soil for many months and survive.
Definitely is old enough to bloom. Give as much full sun as you can.
Keep in touch!