If you do something - especially a test or exam - with flying colours, you do it easily and with great success.
She passed her exams with flying colours!
With all that practice, John will pass his driving test with flying colours.
If something gets off to a flying start, it means it starts very well or very successfully.
Our trip got off to a flying start: the roads were empty, and we got to our destination early.
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.