For the Pokémon franchise's 20th anniversary, Nintendo released the 1st generation games (Red, Blue and Yellow) on the 3DS's virtual console.
They have been updated to use the 3DS's wifi network in order to trade with other players, and reportedly they are also compatible with Pokémon Bank.
Is there any way, with these new capabilities, to transfer a Pokémon between two of these games using only one 3DS?
No, I have the games and can confirm that this is impossible.
Just like any other pre-6th generation game, trading requires two systems as Pokemon Bank is not yet supported, and will only feature one-way transfers (due to obvious reasons) when it is. The wifi trading works exactly as the link cable would have done, so yes two systems are required to trade between any of the 1st generation games.
Unfortunately I do not have the game yet so this is not a definitive answer.
However from the Pokemon website it always uses the word "transfer" and indicates that it can be used to pull the pokemon into the new sun and moon versions (it doesn't even mention pulling them to Gen VI titles). Also it mentions that the same method can be used to "transfer" Gen VI pokemon to sun and moon. Since backwards trading has never been supported I'm going to make an educated guess that you can not trade on red and blue via pokemon bank. That this is a transfer up to pokemon bank (one-way) and no take backs.
