  We construct integrable hierarchies of flows for curves in centroaffine
${\mathbb R}^3$ through a natural pre-symplectic structure on the space of
closed unparametrized starlike curves. We show that the induced evolution
equations for the differential invariants are closely connected with the
Boussinesq hierarchy, and prove that the restricted hierarchy of flows on
curves that project to conics in ${\mathbb{RP}}^2$ induces the
Kaup-Kuperschmidt hierarchy at the curvature level.
