Their hens was not accepted. Should be isn't it?
No, hens are adult female chicken (slepice), kuřata are not adult.
"Hledají jejich kuřata." has the same meaning or not?
It is accepted, but be aware it sounds like they are looking for someone else's chickens.
Unless you make clear you are actually stressing they are looking for THEIR chicken and not someone elses and that's why you are stressing JEJICH.
Okay, it said "sva" could mean "their", "her" and "our", but why is only "their" correct?
Svůj always refers to the subject of the sentence. The subject of this sentence is "they".