1. First, review the phrasal verb break out:
■ (of[concerning] war, fighting or other unpleasant events) △to start suddenly.
- They had escaped to America shortly before war broke out in 1939.
- Fighting had broken out between rival groups of fans.
- Fire broke out during the night.
■ 1. PHRASAL VERB △If something such as war, fighting, or disease breaks out, it begins suddenly.
- He was 29 when war broke out.
- I was in a nightclub in Brixton and a fight broke out.
2. Then, review break out in:
break out in something △to suddenly become covered in something.
- Her face broke out in a rash.
- He broke out in a cold sweat (= for example, through fear).
3. So, break out into can have, in my view, the meaning of suddenly begin some kind of change or becoming, or maybe suddenly get into an unforeseen action:
- I randomly break out into a British accent when I'm speaking. ( source )
- The oligopolies sometimes break out into economic warfare.