Winston churchills speech - we shall fight on the beaches, churchill says 'we shall not flag or fail'
To "flag up" is the uniquely English idiom that comes from the historical idea of using a flag to show what you want to say. British sailing ships, like most other countries, have numerous signal flags representing letters, numbers and even actions to convey information visually across distance.
Another example, ancient armies would conduct battles by raising a certain flag at a specific time, perhaps to signal the cavalry to engage.
Black flags flown in medieval Europe indicated that the plague was present.
Of course nations distinguish themselves by flying specific flags. Perhaps other countries use the phrase "flag up", but I am not aware of it.
After reading the speech, it seems to me that what he meant was that they would never raise the surrender flag.