Italian often uses the definite article where English may not.
So although English says with chicken, Italian naturally says con il pollo.
Here, il pollo means the chicken, but in context it often has a more general sense, like with chicken dishes or with chicken as a food.
This is very common in Italian:
Con means with, so it expresses that the sauce goes well together with chicken.
Per usually means for, so it would change the meaning:
So:
They are related, but not identical.
The standard order here is:
So Questa salsa è buona con il pollo is the most natural neutral order.
You can sometimes move things around for emphasis, but that is less neutral. For example:
This sounds more marked, as if you are emphasizing with chicken specifically.
For a learner, the original word order is the safest choice.
Yes. That would also be correct, but the meaning changes slightly.
Questa points to a specific sauce, often one near you or one already being discussed.
La salsa just refers to the sauce more generally or to a known sauce in the conversation.