I have made panels for the sides of cakes several times and have had trouble with the panels getting wavy.
(like the sides of shoe boxes and beer bottle cakes)
Is there a trick to keeping them nice and flat?
I've never done this before but perhaps you could try letting them partly or fully dry on a flat surface before putting on the sides of the cake?
Yup, if you want them to be very straight, they should be fully dried before going on the cake.