It doesn't evolve by leveling up. You'll need to link trade it to someone for it to evolve. I recommend for a friend to do that for you, not someone you don't trust, in order for them to give it back to you.
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you have trade it to another game and back
you need to catch an Abra then evolve it at level 16 and then trade it and it will evolve into alakazam
Abra always evolves at Lvl 16. Kadabra has to be traded in order to evolve into Alakazam
Kadabra evolves when you trade it to another person
you have to trade to make it evolve into a alaksam