Usage of "Breaking News" over "News Flash" in television news

The term "News Flash" was (and still is) used in the UK to describe an interruption to the normal broadcasting. If a very important news story broke during a time when an entertainment or sports programme was being broadcast the programme was interrupted and someone said "we interrupt this programme to bring you a news flash" - this was followed by an announcement of what had happened.

The phrase "breaking news" is, as you say, used on news programmes to indicate something that is just happening. It is not really an interruption to BBC News or Sky News because they are news programmes.

So a news flash is a news item which interrupts non-news programmes, whereas breaking news is used to describe something just happening in a news programme or channel, which is probably not insignificant but not necessarily important enough to interrupt all other programmes.