Can those characters carry others?

Monkey King:
SPEED SP: EAGLE FORM: Monkey King has "wing symbol".

Gizmo:
TRAIT: TINY TINKERER: Gizmo can use the Flight ability. Give Gizmo a power action and place a light object from outside the game in an adjacent square.

Thanks in advance.

Yes and no. gives the Flight and Carry abilities, the Flight ability itself doesn't let you Carry. So Monkey King can carry and Gizmo can't.

I would say "yes" to monkey king. Because it specifically says MK can use the wing symbol. And the wing symbol grants you Flight and Carry. Unlike Gizmo, his special power just says flight ability.
Monkey King - YES
Gizmo - NO

Thought so, you'd have to possess the symbol itself to gain the Carry.

While Gizmo is just using the Flight portion of the symbol, he doesn't have Carry.

Yep, thanks!