Does Garbodor's "Garbotoxin" Ability shut off Imakuni?'s Doduo's "Frenzied Escape" Pokemon Power?
No, Frenzied Escape is a Pokemon Power, not an Ability.
Source: Evolutions FAQ (2016-11-03), TPCi Rules Team (2016-11-03)

Relevant cards

Note: All applicable cards may not be listed below.
XY12_112
XY9_57
BW11_68
BW6_54
BW9_119