You can do oneway trades. From Firered to Platinum, but not back. You need to get the National Dex and then go to Pal Park on Route 222 below Sandgem Town. Then you can migrate Pokemon from Firered or any GBA game to Platinum.
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In Pokemon firered you can't, but in Pokemon leafgreen you can get it then trade it to Pokemon firered.
Pokemon Emerald: Birth Island Pokemon Sapphire: Trade from Pokemon FireRed, LeafGreen, or Emerald. Pokemon Ruby: Trade from Pokemon FireRed, LeafGreen, or Emerald.
You cannot "trade" pokemon between Pokemon FireRed and Pokemon Pearl. Instead, pokemon from Pokemon FireRed Version can be transferred to Pokemon Pearl via Pal Park.
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Trade it from Pokemon Emerald or Pokemon XD.