A question about kosher rules (meat and dairy)

Okay, so I get you can’t have meat and dairy together because it’s wrong to “boil a kid in its mother’s milk.”

So is it kosher to have chicken and dairy together (assuming both the chicken and dairy are kosher) since chickens don’t produce milk?

Similarly, is it kosher to have beef with goat milk (again, assuming both are kosher) because the kid and mother are of separate species?

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(BTW, I’m not Jewish, just a curious goy :))