By Satin, do you mean a one-generation cross of a silkie and cochin, or the type of bird which, in every aspect except feather type, are identical to silkies?
About a 0-25%. Silkie-feathering is recessive, represented by 'h'. Normal feathering is represented by "H+". (H+/H+) is a bird who has normal feathering, and it will always look identical to a (H+/h) bird in feather type. (H+/h) represents a 'split'; a bird who carries the silkie-feathered gene. You cannot tell visually, so you have to test breed them to see whether they carry the gene.
In an f1 silkie/cochin cross, this would be guaranteed, and you would have a 25% on each chick to get a silkie-feathered bird.
On the Satins which have been bred to look identical to silkies, you cannot guarantee each and every bird is split for silkie-feathering. Some Satins will not carry it, so you'd just have to test breed them to see if you get silkied chicks- if so, congrats, both carry it! If not, well, you've got more test breeding to do to see whether either of them carry it.
(H+/h) x (H+/h) = 50% (H+/h), 25% (H+/H+), 25%(h/h). Aka- 75% normal feathered birds, 25% silkied.
If in doubt, it's best to cross your potential carries to a silkie-feathered bird.
(H+/h) x (h/h) = 50% (H+/h), 50% (h/h).
As for how many generations it'd take to breed a pure silkie or cochin, it varies. Going from an f1 silkie/cochin cross, if you breed enough and cull hard enough, you could theoretically swing either way in as few as 2-3 generations. It'd likely take way longer than that though, if you aren't breeding like crazy. Certain traits can stick around without being seen, then make a problem of themselves by popping up again, and wrecking your progress towards converting the crosses into either breed. Case in hand: I'm sort of trying to do the same thing right now with f2 cochin/silkie crosses(breeding towards being just cochin bantams), and have polydactyly popping up in my chicks even though none of the parents exhibit polydactyly.
From an actual Satin- as in, the birds identical to silkies aside from feather type, I wouldn't even bother trying to breed them into cochins. It'd be a lot of pointless work, and you'd have to be betting on the slim possibility that your breeders carry genes/are impure for the following traits:
Crests
Polydactyly
Fibromelanism
Comb shape
edit: if you were to cross the satins to a cochin, it'd still be a lot of work to breed those listed traits out.
A big bet to be making on slim chances, essentially. Last I heard, Satins were also working towards APA and/or ABA recognition, so why even try turning them into silkies when they're so close to being their own breed?
