First, I should admit, I am a Falcon's fan, and while the general consensus has us attempting to trade UP for Clowney, I wanted to investigate the virtues of trading DOWN.
According to NFL draft trade charts (frequently criticized as outdated, as they were invented by Jimmy Johnson back when he was the Cowboys coach) the Falcon's # 6 pick is worth 1600 "points", but lets work under the assumption that the Falcons would take something slightly less than that in return.
First, I started looking for teams that have shown the willingness to trade up, like the Cowboys, and the Jets.
Next, I looked at these teams resources.
The Jets have the 18th pick, the 49th pic, and the 80th. Additionally, it appears that they will acquire Tampa's third round pick (#69) as part of the Darrelle Revis trade.
Finally, is there a player the Jets would be so interested in that they would want to trade up to the Falcon's #6 spot?
I believe the answer is yes - Sammy Watkins.
Some have suggested he may not make it past the Rams, Browns, and Raiders, the 2nd, 4th, and 5th picks respectively, but with Clowney, Greg Robinson, Jake Matthews, and three QBs all in contention for top five picks, I believe the chance of Watkins being there when the Falcons select are high.