This is fine.

A cape
Seen 34 Minutes Ago
Posted 13 Hours Ago
15,128 posts
11.6 Years
My best guess is that it'll probably work similarly to if you throw two weather Pokemon on the field -- wouldn't the faster Pokemon's ability go first?
Correct, so it'd be the slower one who 'takes over'. That said, I would be surprised if there was any cancelling out here.