Ok, I've written the rules for a three player battle that has been tested a few times and seems fair.
Everybody makes a 60 card deck like usual, the only change to the rules of making a deck is you need at least two basic pokemon instead of one.
determine who is going first randomly, and play continues clockwise.
In your starting hand, you must have at least two basics. If you don't have any, you reshuffle and both opponents draw an extra card (assuming they have basic pokemon). If you have only one basic, you may either reshuffle your whole hand, giving each opponent a card, or play the single basic in front of one of your opponents and reshuffle the rest, drawing 6 cards in your new hand. The opponent you played the basic in front of doesn't draw a card but the other opponent can.
Once everybody has two active pokemon, one facing each opponent, and benched basics are played down, flip over all cards. You may only have 4 pokemon on your bench
In this game you will always have two active pokemon, one for each opponent. Your active pokemon facing opponent 1 cannot attack or affect opponent 2 in any way, including abilities. If a benched pokemon has an ability that would affect another player, you select one opponent for it to effect. If the ability affects all players (for example, Vileplumes ability that says no item cards can be played) it still affects everybody.
On your turn, you may draw one card or two cards. You may attach up to two basic energy or one special energy from your hand in one turn, but you must attach them to different pokemon.
After attaching energys and playing trainers and whatnot, the attacking part of your turn begins. You may attack with both of your active pokemon or just one or none. The pokemon facing opponent 1 attacks opponent 1's active pokemon, and the same for opponent 2.
You can retreat either active pokemon to the bench by paying their retreat cost. Or you can switch your two active pokemon with each other by paying both of their retreat costs. The rule about only retreating once per turn is altered slightly, you can retreat twice per turn, but you can't retreat a pokemon then retreat the pokemon that replaced it. Once a pokemon is placed in front of an opponent, it can't retreat again.
Switch cards can be used to either switch both active pokemon with each other, or one active pokemon with a benched pokemon. Cards that force your opponent to switch cannot be used to switch the opponents two active pokemon, and must switch one on the bench.
This format doesn't use prize cards, but rather each player has 6 K.O. points (just use a die or tokens to symbolize this) Every time your pokemon is knocked out, you lose one K.O. point. If you are out of K.O. points, you are defeated. (more on this later). the player who knocked out your pokemon draws the top card of their deck as a "prize card".
If you run out of cards in the deck you continue playing, but obviously your game is seriously hindered because you are stuck with the cards you have and cannot draw any more. (I'm still iffy on this rule, if people could test it both ways and reply, that would be helpful!)
If your active pokemon is knocked out and you have no pokemon on the bench to replace it, you do not lose immediately. Immediately begin flipping over the top card of your deck and discarding it until you get a basic, this basic is your new active pokemon.
If you cannot have two active pokemon, because you ran out and your deck is discarded, you are out. If you run out of K.O. points, you are out.
If a player is out, the remaining players choose one of their active pokemon to go to the bench, the other remains as their active pokemon. Continue battling with standard rules, excepting conditions of victory, until one player runs out of K.O. points.
That's what I've got, sorry if it is a bit complicated. If anyone can find a way to reduce teaming up on one player in this playstile, do tell!