Position racks in the upper and lower thirds of the oven; preheat to 375 degrees F. Put 2 heaping cups potato chips in a large bowl and add the semisweet and caramel milk chocolates; set aside. Put the remaining 3 cups potato chips in a resealable plastic bag and finely crush with the bottom of a measuring cup; transfer to a small bowl and set aside.
Whisk the flour, baking powder, baking soda and kosher salt in a medium bowl. Beat the butter, granulated sugar and brown sugar in a large bowl with a mixer on high speed until very fluffy, about 5 minutes. Add the eggs, one at a time, then add the vanilla, beating well after each addition until creamy. Reduce the mixer speed to low; gradually beat in the flour mixture until combined. Add the potato chip?chocolate mixture and beat until combined.
Roll the dough into large balls (about 1/4 cup dough each), then roll in the crushed potato chips. Arrange 2 inches apart on 3 unlined baking sheets. Bake, switching the pans halfway through, until the cookies are browned around the edges but still soft, 20 to 22 minutes. Immediately sprinkle with flaky sea salt. Transfer the pans to racks and let cool 10 minutes, then slide a spatula under the cookies and transfer to the racks to cool completely.