What is the best type of plant for covering a 165ft chain link fence?

I live in Miami, we use Clusia for just about all privacy. We have tons of nurseries in the area that offer bulk pricing on them. They grow quick and bushy.

http://www.south-florida-plant-guide.com/clusia.html

Here's a picture of them. But the link I posted above gives you more information. although they say to space them 5 feet apart, the ones I have in my yard were space 1 and half feet apart so they would create true privacy.

Try bougainvillea. It gets thick (privacy), gives gorgeous flowers in many colors, is thorny (unwanted animals) and LOVES tropical heat.

The fence companies also sell a faux plant covering that attaches to the fence - it stays green and in place all year, never needs trimming and heavy rain or drought don't damage it. We tried it and love it, plus it can be removed easily for fence repair or for moving a section of fence.

I would plant a couple of Carolina Jasmine. The will spread over the fence and fill it in pretty quickly.

Ivy is really fast growing and you can get a couple of pieces and it will grow in one season. I think you said you were in Florida so it should stay green year round.

A few clematis different colors will be nice

There is a flowering vine called Bridal Veil that will cover a fence very densely in a year. It has really pretty petite white flowers and it gets fuller, thicker and denser every year.

Don't plant something invasive like bamboo, whisteria, english ivy, virginia creeper or a few others. These can very easily get out of hand and become your neighbor's problem also. We have been fighting the english ivy our neighbors planted many years ago.