Normally I do not put a male and a female together until they are a year old ... I do know some breeders that do put them together as early as 8 or 9 months old ... but ... the female should weigh at least 600 grams before you put her in with a male chinchilla.
Some breed in colonies, some breed in runs and some breed in pairs.
A colony is one male to 2 or more females in the same cage.
A run is where each has their own cage, but the male has access to each of the female's cage by way of a run or tunnel. When this is done, the females have to wear a collar that keeps them from being able to get out of their cage and into another female's cage. Some females will kill the kits of other females or will fight with other females.
In pair breeding 1 male and 1 female live together all the time.
Since you have two females and one male, you might want to think about letting the male have one female, then when they have a male kit, it could be matched with the other female.
If you let the one male mate with both females, then all the kits produced would be closely related.
Just something to think about.
Jo Ann