I am a Chinese citizen living in England. I have a PRC passport with a UK visa. I plan to go on holiday to Northern Ireland soon and will travel there by plane. Is there anything I should bring other than my passport in order to be allowed to board the flight?
You should bring your passport, you don't need anything in addition to this.
Northern Ireland is part of the UK, so it's a domestic trip with no "immigration" or similar.
However, almost all airlines require passengers to have photo ID (for their own commercial reasons - basically to ensure that person flying is the same as the person named on the ticket) and a passport is the best form of photo ID for a non-European citizen to use.