From: http://www.bbc.co.uk/worldservice/learningenglish/language/2013/08/130815_todays_phrase_with_flying_colours.shtml
With flying colours
Today's Phrase
If you do something - especially a test or exam - with flying colours, you do it easily and with great success.
Examples:
She passed her exams with flying colours!
With all that practice, John will pass his driving test with flying colours.
Take note
If something gets off to a flying start, it means it starts very well or very successfully.
Example:
Our trip got off to a flying start: the roads were empty, and we got to our destination early.
Interesting fact
The origin of the phrase 'with flying colours' relates to ships' flags. A long time ago, ships coming into port flew coloured flags, to show people how successful their voyage had been.