Security implication of deriving key with fixed salt for files authentication
For that purpose, are there some security implications having that
  salt as a fixed byte string?


The key re-use is fine here, because the standard model for MACs allows the attacker to request an arbitrary (polynomially bounded) amount of authenticated messages while still not being able to forge new MACs.

As a bonus, you may want to consider using the built-in MAC mode for Blake2, because it reduces code complexity and improves speed while providing a comparable security level (thanks to Richie here)