The best picks not in lane to counter Kayle include Zeri, Kalista, and Samira. These champs are all good at countering Kayle with win rates over 58%. Even if these Kayle counter picks are not picked in your lane, it's not a good idea to choose her into one of these matchups. They will often win against Kayle.
Yet, if the other team picks either Rumble or Brand, Kayle mains should strongly consider taking her, as she easily beats these champs with win rates over 54% against both ofthem.