Chinchillas are agouti "A" which gives the banding to the coat and chinchilla "cchd" which removes all red pigment from the coat.
The chinchilla mutation was originally carried by the wild european rabbit that our domestic rabbits originated from. The chin mutation was discovered in domestic rabbits in the early 1900's thorugh inbreeding. Most breeds probably introduced the chinchilla color through the chinchilla breed itself. In developing new breeds now, many small breeds use the Netherland Dwarf or Mini Rex to introduce chin to their gene pool. Larger breeds can use the Satin or Chin breeds as well as the Flemish.
It's best to breed chin to chin if you want to get chins. Mixing with other colors may also give you poor chin color.
If you cross to black or blue, you'd most likely get chestnut offspring because the "A" agouti is dominant, but the chin "cchd" is recessive.
Pam