A list of popular flowering vines:-common names are followed by the latin and predominant flower colour is within the square brackets

Chocolate Vine Akebia (Lardizabalaceae) quinata [purple/brown flowers]
Trumpet Vine Campsis grandiflora (chinensis)  [orange/red]
Trumpet Vine Campsis radicans Atropurpurea  [scarlet]
Madame Galen Trumpet Vine Campsis tagliabuana [salmon red]
China blue Vine Holboellia (Lardizabalaceae) coriacea [blue]
Climbing Hydrangea Hydrangea (Hydrangeaceae) petiolaris [white]
Summer Pink Jasmine Jasminum (oleaceae) stephanese [pink]
Winter Jasmine Jasminum Nudiflorum [yellow]
White Jasmine Jasminum Officinale [white]
Pink Jasmine Jasminum Polyanthum [pink]
Scarlet Trumpet Honeysuckle Lonicera brownii Dropmore [scarlet]
Honeysuckle Lonicera etrusca  [creamy yellow]
Gold Flame Honeysuckle Lonicera heckrotti [orange/purpley crimson]
Hall’s Honeysuckle Lonicera japonica Halliana  [white to nude]
Mandarin Honeysuckle Lonicera Mandarin [orangey yellow]
Early Dutch Honeysuckle Lonicera perclymenum Belgica
Late Dutch Honeysuckle Lonicera perclymenum Serotina [red/purple white]
Honeysuckle Lonicera tragophylla [yellow]
Chileon Jasmine Mandevilla (Apocynaceae) suaveolens  [white]
Blue Passion Flower Passiflora (Passifloaceae) caerulea  [purpley white/green]
Lady Amethyst Passion Flower Passiflora Lavender [lavender purple]
Aubertii Silverlace Vine Polygonum (Polygonaceae)  [white]
Star Jasmine or (Confederate Jasmine) Trachelospermum Jasminoides  [white]