For anyone else, maybe a picture will help. In the picture, I lifted up the smaller frill so you can see the sleeve piece below it.

After gathering the tops of both frills, the biggest frill is attached to the lower side of the sleeve pieces. The smaller frill just is basted on top of the sleeve at the neckline. The neckline binding goes over both of them.

In the gathering, the smaller frill needs to be gathered to the size of the top of the sleeve where it attaches to the neckline binding. The bigger frill needs to be gathered to the size of the lower end of the sleeve piece, where it attaches.