As per years of Star Wars Extended Universe canon, the GFFA definitely has a Galactic Standard Year. While much of this is now 'Legends', the year convention of "[Years] After Battle of Yavin" and "[Years] Before Battle of Yavin" seems to still be canon, which means definitely standard years exist, and as per Legends this was Coruscant Standard Year (365 standard days of 24 standard hours), presumably based on the revolution of the galactic capital.
Kashyyk has been a Republic planet for many many years, so there's no more reason to assume that Chewbacca is telling his age in Kashyyk solar years, rather than Galactic Standard than there would be to assume that a random person telling you the time is telling the local solar time as opposed to standard time-zone time.
As per Legends, a Wookie's average lifespan is 400 (Galactic Standard) years. Chewie was born 200 BBY, and since the new movie trailer seems to corroborate that, that means the 200 BBY date of birth for Chewie is canon again.
(Btw: It seems to be canon again that Kashyyks' orbital period is 381 (galactic standard) days but this has nothing to do with Chewie's age)