We can only measure our speed relative to other galaxies and establish that for larger and larger scales, we have no net 'peculiar' motion with respect to them, AND with respect to the expansion of the universe itself. The cosmic background radiation establishes for us the local frame of reference which is moving with the expansion of the universe, and the Earth+Sun+Milky Way does have a net velocity with respect to this which generates a 'dipole' anisotropy in the otherwise smooth cosmic background radiation. But that's the best we can do to establish our net motion in the universe.