Right okay, so the mum is chinchilla coloured, the dad I think is a chocolate agouti (or cinnamon whichever you want to call it) but even if he’s just a regular agouti this still applies
Chinchilla = A_B_Cchd_D_E_
Chocolate Agouti = A_bbC_D_E_
Black Otter = At_B_C_D_E
Right so firstly A (agouti) is dominant to At (tan) and a (self) so both parents must be carriers of At or a, cross the two together and you could get AA, AAt, Aa, AtAt or Aa. The black otter is either AtAt or Ata
B is the black allele, b is the chocolate allele so your black otter must have at least one copy of the B allele making the dominant black colour show through
The colour gene is more complicated. C (full colour) is dominant to Ch (Himalayan) which is dominant to Cchd (chinchilla dark) which is dominant to Cchl (chinchilla light/sable) which is dominant to c (albino). The dad has the most dominant allele, C and this is what your other has inherited.
So yeah the parents have an interesting mix of genes, mum could be AAtBBCchdCchdD_E_ and dad could be AabbCcD_E but unless you know the colours of the other babies or the grandparents it’s impossible to say. But black otter is definitely possible as long as both parents carry the At or a gene