Zinc Oxide may not work in your circumstance after reconsidering your other dog licks the ears.
My dog has ear infections, but even with medication it has been hard to get rid of. I'm always reading up on things and came across an article about using Pellitol in the ears - it helps "draw" infection/debris, etc. Well....Pellitol is no longer on the market...but there was a follow-up article that described the ingredients. It said to ask your vet to scribe it so a compounding pharmacy could make the concoction. This is pricey for me, so, looking over the ingredient list Zinc Oxide is first on the list - I have thought about sourcing some of the other ingredients to see if I could make something better than the diaper rash cream I have
. Anyway - I clean my dogs ears daily, they are pretty bad, I do put Zinc Oxide on the interior flaps and wipe a very small amount in the "hole" with a qtip- just where the yuck bubbles up. It does seem to draw and dry up some of the infection, plus protect the skin from irritation of drainage. But of course he can't lick his ears. This is just something I do - I'm not a vet - I don't put the cream way down in his ear either.The Vinegar may be a better route to go for you since you have the other dog licking all the time.
https://www.whole-dog-journal.com/issues/7_6/features/Canine-Ear-Infections_5642-1.html
(update on ingredients) http://www.whole-dog-journal.com/issues/16_11/features/alternative-treatments-updated_20861-1.html
