you can't the versus seeker doesn't work in the gym buildings trust me i have tried
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Unfortunately, you cannot. Once you defeat them, you cannot have a rematch. However, if you want a better challenge, you could rematch the Elite Four. They will definitely level up your Pokemon.
You can buy them anywhere, but you have to beat some gyms. That makes the Pokemarts get new items.
They will call you on the Pokenav and say that the gym is ready. Don't get your hopes up, I got my first rematch about 6 months ago and I still have 3 or 4 left to beat again.
In Pokemon firered you can't, but in Pokemon leafgreen you can get it then trade it to Pokemon firered.