How do I hide a chain-link fence with vines or shrubs?

Ninebark, forsythia, privet, Autumn Clematis, etc.

Depends upon your location and growing conditions.

Contact a local nursery or master gardener, taking photos of your property with you.

Be prepared to divulge drainage, soil, sun or shade, animal issues, trees, etc.

Clematis, if you've for the right conditions, would be great.

I would try jasmine.it will grow fast so be sure your fence will support the weight.

Any clematis or climbing rose would be good, you could also to for honesycle or forsithia bushes.

English ivy can grow just about anywhere and is fast growing. But can get out of hand if you let it.