We show that two-terminal transport can measure the Luttinger liquid (LL) parameter K, in helical LLs at the edges of two-dimensional topological insulators (TIs) with Rashba spin-orbit coupling. We consider a Coulomb drag geometry with two coplanar TIs and short-ranged spin-flip interedge scattering. Current injected into one edge loop induces circulation in the second, which floats without leads. In the low-temperature (T→0) perfect drag regime, the conductance is (e2/h)(2K+1)/(K+1). At higher T, we predict a conductivity ∼T−4K+3. The conductivity for a single edge is also computed.