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).
I believe this is the default comprehension. The sentence mentions my friend ("мій друг"), performing an action of traveling ("подорожував") with someone referred to as "brother" ("з братом"). This produces an ambiguity whether the "brother" is a speaker's brother or a friend's one. In Russian (my native language) and (I believe) in Ukrainian as well, the default comprehension is to relate "brother" to sentence's subject ("мій друг") and not the speaker. For the latter case you are likely to get an explicit clarification: "мій друг подорожував з моїм братом", or even a sentence that describes both friend and brother as "my" people, as in "мої брат з другом подорожували"