The triplet 'fire and blood and anguish' are the Inspector's final words before saying 'Goodnight'. They are part of a speech in the style of a sermon, his final attempt to get all the Birlings to accept the lesson that, 'We don't live alone. We are members of one body. We are responsible for each other.' The upper class Birlings have not observed this lesson in their dealings with the working class Eva Smith; they have not acted responsibly to their fellow human being, for example making her redundant or denying her financial aid without any concern for her future.
The conclusion of this sermon is 'if men will not learn that lesson, then they will be taught it in fire and blood and anguish'. This is a reference to War for two reasons: firstly, because the individual words of the triplet make us think of hell, bloodshed and sorrow for loss of life which together define War.
The second reason is to do with Time. The play is set in 1912 with Mr Birlings complacently of the opinion that there is no possibility of war.The First World War broke out in 1914. Also the play was first performed in 1946 just after World War 2 had finished. Priestley is telling the audience they mustn't be complacent: there will always be wars until we learn to live together as one.