In this paper, we introduce a flip operation on self-complementary ideals of chain product posets and study the resulting flip graphs. We give asymptotics for the number of vertices in these graphs, compute their diameters, and give bounds for their radii. We also define similar flip operations on self-complementary ideals of the chain product $[2r]\times [2r]\times [2r]$ satisfying additional symmetries, and we achieve similar results for the resulting flip graphs.