Formerly, in military contexts, flying colours meant having the regimental flag flying as a sign of success or victory
A conquered army usually had to lower (or strike) its colours
Related Idioms :
lend colour to = give colour to
make something seem true or probable
1991 - J. Rusbridger - The Intelligence Game - Nothing should be done that would lend colour to any suggestion that it [the Security Service] is concerned with the interests of any particular section of the community.
see the colour of his money
receive some evidence of forthcoming payment from a person.
nail your colours to the mast = pin your colours to the mast
declare openly and firmly what you believe or favour.
sail under false colours
disguise your true nature or intentions
show your true colours
reveal your real character or intentions, especially when these are disreputable or dishonourable
The distinguishing ensign or flag of a ship or regiment was known as its colours and the word is used in this sense in these four idioms.
A ship on illegal business or in time of war may fly a bogus flag in order to deceive and would therefore be sailing under false colours.