Short answer, Yes you can Sneak Attack someone who is running away. But there are some circumstantial issues.
Here are the rules for running:
You can run as a full-round action. If you do, you do not also get a 5-foot step. When you run, you can move up to four times your speed in a straight line (or three times your speed if you're in heavy armor). You lose any Dexterity bonus to AC unless you have the Run feat.
You can run for a number of rounds equal to your Constitution score, but after that you must make a DC 10 Constitution check to continue running. You must check again each round in which you continue to run, and the DC of this check increases by 1 for each check you have made. When you fail this check, you must stop running. A character who has run to his limit must rest for 1 minute (10 rounds) before running again. During a rest period, a character can move no faster than a normal move action.
You can't run across difficult terrain or if you can't see where you're going.
A run represents a speed of about 13 miles per hour for an unencumbered human.
Flat-footed is a very specific condition that only happens in the first rounds of combat before a combatant has taken an action. However, as you can see the target is in fact denied his Dex bonus to AC which does grant you the ability to Sneak Attack him.
Two things that might still prevent you from Sneak Attacking a running target are: Distance and the Run Feat. Ranged Sneak Attacks can only be accurately made out to a distance of 30 feet, so if your target is further than that you won't have the accuracy to Sneak Attack him even though he is denied his Dex bonus to AC. (Exception to distance would be the Sniper Shot Achievement Feat which increases the distance at which you can make precision based damage.) If your target has taken the Run Feat you will not be able to apply Sneak Attack damage to him from running alone due to the fact that he no longer loses his Dex bonus to AC when he is running.