Background
There is a fundamental difference between the English labels "transitive" / "intransitive" and the Japanese labels 他動詞【たどうし】 / 自動詞【じどうし】. Please read the thread about that here:
Key point: 自動詞【じどうし】 can sometimes have a syntactic (based on the grammatical structure of the sentence) object.
Your question
With regard to your question, can を work as から in certain situations, the best answer is "kind of". :)
The verb 飛【と】び出【だ】す is often glossed as something like "fly out from, fly away from". In this translation, it is reasonable to expect から.
It can also mean "to leave (in the particular fashion of flying out)". An analogy in English is that word "leave". We can say "we leave from a place", using a construction similar to how から works in Japanese. We can also say "we leave a place", which is similar to how the を works in Japanese in your sample sentence.
Note that there are other 自動詞【じどうし】 constructions that also take を, and where that を doesn't work as から. Consider 道【みち】を[歩く]{あるく}. We can say something similar in English as "I walk along the road", and also as "I walk the road", using "the road" as the direct object of "walk". There is a fuller discussion of the use of を with 自動詞【じどうし】 in this thread: