If I had to do an ugly chain link fence. Confederate Jasmine is an evergreen flowering vine, drought tolerant once established. It does not clump at the top, so would be ideal for covering a chain link fence year round.
Vines for chain link suggestions: Covering the chain link fence is a splendid idea, but even chain link has its load limits.Honeysuckle, trumpet vines are 2 that will cause it to sag. I don't use heavy vines. Hyacinth Bean, Cardinal climber, Blackeyed Susan,Clemitis are great for the chain link. If you are stuck on vines, avoid the trumpet vine, passionfruit, ivy, and ficus. I would go with star jasmine. It's ubiquitous for a reason.