Answer: Most of the drought-tolerant annual vines I can think of have blossoms, but perennial vines such as Virginia Creeper may work; the latter can become invasive. You may be able to maintain a variety of English Ivy (Hedera helix), such as the Burpee selection 'Thorndale' which is very hardy. You can increase your chances of success by adding Terra Sorb. The inert polymer takes up water and holds it for plants to absorb when needed. You won't have to water as often, and plants will have access to much needed moisture during the heat of the day.
If you don't mind if the vines have little blooms, consider canary creeper (Tropaeolum peregrinum), which has interesting 5-lobed leaves, Jewel of Africa trailing nasturtuim, which has green and white variegated leaves and a mix of yellow, red, cream and pink blooms, or Hyacinth Bean Vine or Scarlet Runner Bean. The beans have smaller, less distinct flowers. Hope this is helpful!
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