This paper studies the chromatic number of the following four flip graphs (under suitable definitions of a flip):

• the flip graph of perfect matchings of a complete graph of even order,
• the flip graph of triangulations of a convex polygon (the associahedron),
• the flip graph of non-crossing Hamiltonian paths of a set of points in convex position, and
• the flip graph of triangles in a convex point set.

We give tight bounds for the latter two cases and upper bounds for the first two.