>From Pokémon Emerald onwards, if a Pokémon with this Ability is leading the party, there is a 50% chance that wild Pokémon encountered will have the same Nature as the Pokémon with Synchronize.
Considering this it only works for the Pokemon in the first slot, so even in double battles the second Alakazam wouldn't matter because it is in the second slot.
If it did work and both Alakazam's Synchronize worked it would probably just be random as to which of the two natures it got(if they had different ones to begin with).
Source
Hope I helped.