What is the verb that means 'to fly a flag'?

I'm pretty sure it's used in the navy, and it could be used in the sentance that ship is ~. This has been bothering me for a long time!

flying its colours

I think the phrase you are looking for is that ship has colors. Otherwise, a ship either raises, posts, or flies it's colors. I hope this is of some help to you.

You might be looking for strike its colors which means to take them down. A ship will do this when it surrenders.

You can hoist a flag or a sail. You can unfurl a flag or sail.