You may find it more effective to give monsters new traits or powers.
In terms of flanking, there is a theme called Stormraider that does something similar:
Stormraider Level 10 Feature (10th level): If you and one or more allies are adjacent to an enemy, you and those allies are considered to be flanking that enemy.
It's not much of a stretch for a DM to take this feature and hand it out to monsters that need it without having to globally affect the flanking mechanics for all monsters and players.
Another power I've sometimes seen on monsters is a power that specifically discourages flanking. Consider this power from Gurrak, Ettin Headtaker (H3: Pyramid of Shadows):
Swat (immediate reaction, when an enemy moves into a position that flanks the ettin, at-will)
The ettin targets one creature flanking it; +13 vs Fortitude; the target is pushed 3 squares.
And you can always just make your monsters immune to being flanked, like the Hydra:
Enemies can’t gain combat advantage by flanking the hydra.
If you want to make players move more, focus on movement!
If you want to shake up players, you might want to find more explicit movement-related solutions. Forced movement is an obvious one: put some monsters with
Pull powers to yank players out of the line, or an enemy controller with an Area Burst 1 or 2 with
Slide to scramble things around.
A more creative solution might be to come up with monsters that afflict players with effects that make them move around. For example, an artillery monster that afflicts ongoing 5 fire (save ends) to the target and each creature adjacent to it. Now the players will want to make sure they're not adjacent to that character, but that character has an interesting tactical effect he can apply to enemies.
In general though, find specific solutions for specific problems.
If the problem is a common formation, address that formation directly rather than changing mechanics that could have unforeseen consequences in other areas of the game.