They are a whole, complete plant and as such will flower when they feel conditions are right. The flower is to make seeds. Most plants have more than one strategy for propegation of their genes. :)

Sweet potatoes are a member of the morning glory group. Some varieties blossom with abandon others rarely. As sunnibel stated They have to seed in order to get crosses an start new varieties. Covington flowers abundantly.
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I think sweet potato flowers are beautiful. I don't see many of them, but I love 'em. Haven't seen one this year "yet" on mine.

I agree the flowers are prety. I have a large bed of sweet potatoes plants. The plants are very green healthy and look happy. There are over 50 flowers in the bed. The neighbor's wife and her friend asked me if they can come close and look at them and take pictures I said sure. I Had sweet potatoes last year but did not flower. I love eating sweet potatoes.
Abe