It is. See the source provided above. Technically the ΛCDM universe follows the FLRW metric, but if you look at its line element, you'll see it's usually just Minkowski in spherical coordinates times a scale factor (capturing the expansion) for spacelike coordinates:

ds^2 = -dt^2 + a(t)^2 dΣ^2.

Note that a scale factor that affects all spacial coordinates the same does not induce curvature. The generalised form of the FLRW metric includes a 1/(1-k) factor for the radial coordinate, but the curvature k for our actual universe is measured to be 0 within experimental precision, which, again, is a mystery. There's no good reason why a universe containing matter/energy should be globally flat (*cough* inflation). Factor out a(t) in a line integral and you'll get comoving distances over more or less euclidean space, i.e. the common format in cosmology literature. Things like luminosity distances are more interesting when you e.g. want to know the absolute magnitude of a far away object, but that doesn't really make sense for the CMB.

>Probably the most widely used distance measure, from Earth's perspective, is redshift.

Redshift is used to measure these distances sans any reasonable alternatives. But when you want to make e.g. a map, you can't use redshift (or proper distance for that matter), unless you want your map to be distorted.