In late 1775, the 'revolting' Colonies chose a flag with colours that reflected their feeling of unity with the Mother Country, (hence the adoption of colours on the Union flag) but which also expressed their demand to obtain justice and liberty - (which is where a different design and the stars came in).
When the flag was fomally recognised after Independence the significance of the colors was defined: "White signifies Purity and Innocence; Red, Hardiness and Valor; Blue. Vigilance, Perseverance and Justice."