Can't speak for Duxford but at Old Warden the only role for the FISO on the radio is to advise pilots if the show is on time and acknowledge calls such as start up calls and radio checks. Aircraft will often call "final pass" etc. to advise that their display is completing. Aircraft occasionally make calls which help co-ordination during multiple aircraft displays.
Thankfully I have never been present at an accident so no idea what happens then. I imagine there is an accident plan. have been present at a land out when the call was simply "Gladiator landing out".
US radio practice is a bit different to the U.K. where I adhere strictly to be the CAPs (413 and 452 for me as an A/G operator). It tends to be a bit more relaxed.