My friend was travelling with his brother - does that work, or does it require a different form of подорожував?
Ukrainian usually doesn't make any difference between simple and continuous tenses (unless you need to emphasize the duration of the action somehow, then a participle may be used, but in modern Ukrainian present participles are so rare, that most times if you use it it will be considered a mistake; usually other means kick in, e. g. time-specifying adverbs and other descriptive phrases).
suppose i am talking talking about my friend thomas traveling with the brother of my friend anna, to the effect that i am saying "my friend traveled with her (anna's) brother". how might i state that in ukrainian i am wondering?
You are mix up here. Мій друг is a male friend and іі is her. For іі it would have to say Моя подруга
An example (наприклад): A telephone conversation (телефонну розмову) Mama: Привіт! P8C: Привіт, мама! Ти знаєш моя подруга Анна? Мама: Так. P8C: Мій друг Tomac подожував з її братом.
Is this something like what you were wondering?