I'm not sure there's a specific source, though there's no shortage of pilot autobiographies and collected accounts with snippets that give an idea of the sort of messages exchanged. Of the former Geoff Wellum's First Light is exceptional, and includes a fair amount of dialogue (albeit written a fair bit later); of the latter they span from e.g. Ten Fighter Boys, written and published contemporaneously, Norman Gelb's Scramble: A Narrative History of the Battle of Britain, Max Arthur's 70th Anniversary Last of the Few etc. In fiction the 1969 film had plenty of RAF veteran advisers so, taking account of dramatic license, shouldn't be too far off the mark; on the book front Derek Robinson's Piece of Cake is pretty well regarded.

One thing to bear in mind is that accounts, especially those for wider consumption, tend to be somewhat sanitised: "In the beginning, we tried to get the girls to leave those rooms in which R/T was broadcast from the aircraft during air fighting - for the language was terrible. But it wasn't idle blasphemy or obscenity. It was the voice of men in the midst of fighting for their lives - and dying. The girls refused to leave their jobs and said that they didn't mind the language as much as we thought. They added that it was nice of us to think of their being like that, all the same." (Gerald Gibbs in Scramble: A Narrative History of the Battle of Britain)

I think your best bet is to get your hands on the appropriate RAF Air Publication (AP). The RAF pretty much had a manual for everything, although these would obviously not include informal exchanges.
I've looked around for you but I don't seem able to find a digital version.
I believe you're after: AP 3024, Flying control in the Royal Air Force