Will Hubble's law always be accurate?
As per the above comments, there will still be v=Hd, if v is the rate of change of current distance, and d is the current distance-- as long as the universe continues to obey the cosmological principle.  The nearby version of that will still look like correlating Doppler-shift velocity to distance indicators, and the faraway version will require a dynamical model, albeit a very simple one due to dark energy.  It will lead to a constant H that will not be anything like the inverse of the age of the universe.  And if you go too far into the future, you won't be able to see the CMB, or quasars, so alien cosmology will really struggle.