Fence trellis with flowering vines, must bloom all summer. Options: morning glory, Honeysuckle ( 'Scentsation',’ shown here, is a non-invasive honeysuckle that’s lovely when trained on fences or trellises.), kiwiberry, Akebia or Chocolate Vine (Hardy in Zones 4-8.)
hgtv
Tangerine Slice A-Peel Black-Eyed Susan Vine(bloom all summer, Annual vine, hardy in Zones 10-11.) hgtv

"Annual vines are generally better for continuous bloom."

Moonflower

Mckenzie climbers: Mirabilis(4 o'clock-bloom July-frost), black-eyed susan vine(thunbergia all summer bloom), moonflower(blooms evening-noon, cloudy days), Cypress vine (Ipomoea quamoclit, flowers open all day-bloom July-frost), Tall Climbing Mix Nasturtiums(all summer bloom)

Lobelia- flows down, not a climber, bloom June-frost. Uharvest also has trailing(climbing)nasturtiums.