TEs aren't needed if you are only going to be running the flexbone exclusively, if you add some pistol formations then you'll want to look into them.
There is no fullback in the flexbone, there's the A-Back and the B-Back, the B-Back lines up behind the QB and the A-Backs line up on the wings (in the game A-Backs are running backs), but in both situations they are running backs with different specialties.
You want A-Backs to be fast, but they should also be decent run-blockers (they will need to be able to throw a block on the edge to free the ball carrier), when you pass out of the Flexbone they are going to be running routes so it doesn't hurt for them to be good pass catchers either.
B-Backs are powerbacks, it should be very interesting seeing how the new speed burst mechanic works this year because that is a big part of their game. They power through the line and then turn it up in the open field. The ideal B-Back is a guy like Jonathan Dwyer, he's put on some weight since entering the pros and it has effected his speed but at the college level he was the perfect example. The ability to run over players and kick it into that next gear as soon as you see daylight. Acceleration is something you will want to look at for this purpose, it can be the difference between churning out medium gains and game-changing plays.
It is not a bad idea to look at Fullbacks for the system, bruisers who can grind out yards while your primary guy is taking a breather, having a guy like this is much more efficient than wasting another RB who could be lining up at A-Back for you. These guys could also line-up at TE if you choose to run out of the pistol for a change of pace.
WRs need to be able to block, if you can get a game-changing WR (say some hot-shot is really interested in your school) go after him hard, guys like that really open up the offense. Demaryius Thomas soared to the top WR taken in the 2010 draft because of what he did his Junior year in this offense, and its why a guy like Stephen Hill went from a late-round pick to a potential 1st rounder (ultimately drafted in the 2nd), they will get open so if you have a WR who can out jump or out-run the defense all you have to do is get the ball to him. Outside of that the main attributes will be catching and blocking, you're going to want fast guys but most importantly you are going to want guys who will catch the ball when you throw it to them (it really hurts a drive when the play goes well and the guy can't hold onto the ball, that was the story for Tech in 2010).