"My friend traveled with his brother."
Translation:Мій друг подорожував з братом.
While in English you usually need to put possesive pronoun when speaking about relatives, there's no such rule in Ukrainan. "His" is implied. But if you really need to specify, it's better to say зі своїм братом. Свій/своя/своє/свої means belonging to the subject (whatever the subject is)