I know it can have extremespeed from a pokémon Box event with pickup, but how come it can't pass it through breeding to have a gluttony extremespeed zigzagoon?
No, it cannot have ExtremeSpeed and Gluttony.
ExtremeSpeed Zigzagoon's abilty is Pickup. So it can't Gluttony in that case. And ExtremeSpeed is not an egg move for Zigzagoon, so it cannot be passed down.
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