If my opponent's Dolliv attacks with "Apply Oil" then on my turn I switch to a new Active Pokemon, do I still have to flip a coin to successfully attack?
No. Even though the effect references the opponent it was placed on "the Defending Pokemon", so the effect went away when you changed your Active Pokemon.
Source: Scarlet & Violet FAQ; TPCi Rules Team (2023-03-30)

Relevant cards

Note: All applicable cards may not be listed below.
SV1_22
SV1_22