If you review the Permethrin Label, you'll see there is a wide range of mixture rates. In general, 2-4 oz will cover most any flying insect pest. So I would say to go with 2 oz per gallon if you're doing a maintenance spray. This type of spray is what you'll do whether you're seeing insect pests or not. In other words, if you're treating to make sure you don't get any pests, using just 2 oz per gallon will be fine.
But if you have an active problem, 4 oz per gallon or even more is acceptable in order to get a quick knockdown of the targeted pest. Permethrin can be mixed stronger as the label shows as much as 6 oz can be used per gallon of water if needed.
Permethrin 10: https://www.bugspraycart.com/insecticide/liquid/permethrin-10