Here's a flag for Virginia I did a while back:
This one is the city flag of Richmond with the central boatman design replaced by a Tudor rose. Now, allow me to grasp at straws as I attempt to extract symbolism:
The Tudor rose symbolizes Queen Elizabeth I, the namesake of the state, and its English colonial heritage in general. More obscurely, the rose is also the national flower of the US (who knew, right?) so it sort of alludes to Virginia's important role in the country's founding. The rose also happens to be shaped like a pentagon, and of course the Pentagon is located in Virginia, as is much of the federal government, so there's an additional allusion.
In the flag of Richmond the nine stars are meant to symbolize the nine states that were formed from Virginia's original territorial name, hence Virginia's nickname "Mother of States", symbolism that carries over nicely here. If you consider the rose as a tenth star it could also represent Virginia's position as the tenth state to ratify the Constitution. And the circular shape recalls the Betsy Ross flag, and we all know how important Virginia was in the Revolution...
As for the stripes... well, they resemble the stripes on George Washington's coat of arms that were adapted into the flag of Washington DC, so it could represent both George Washington's Virginian origins and Virginia's proximity to Washington DC. And the two blood-red stripes could also represent the Revolutionary and Civil Wars, two of the bloodiest and most important wars in American history that were fought on American soil. And if you count the white stripes then there's four stripes, representing the four presidents of the Virginia Dynasty?
Anyway, I think it works.