Use conditional branches to check which pokemon you picked and which pokemon your rivals will pick.
Ex)
You pick pokemon n1 - set variable: Choosen pokemon to 1
Conditional branch to see which pokemon you choose
make Rival 1 pick a pokemon - set variable Rival 1 to pkmn you make him choose
Conditional branch to check which pkmn the player and Rival 1 choose
make RIval 2 pick another pokemon
.
.
.
Is that simple. If you want something more complex then you could use random variable for each rival to make rivals pick randoms pokemons after the player picked his pokemon. This way you would make players have different experiences, even if they pick the same pokemon over and over again. Beware that, if you do this, you will have A LOT of trouble in the long run. Because you will have to make teams for every Rival and for every one of 6 pokemons available making a total of 30 teams, this only at the start! It probably would make you crazy, even if it sounds like a nice idea, it isn't my thing to waste my time making that much of things.
I just made it by mind. But I guess you can have a general idea of what I tried to make here.