Virginia Postrel also writes about the Georgia elections and what they may have had to do with the flag change there; she links to an article in Metropolis magazine talking about how the flags' design could have been an issue in their success or failure.
At least in Mississippi, that didn't make a difference. A former colleague, D'Andra Orey, took a look at the issue and found racial attitudes were the prime factor on how people viewed the flag issue. The fact that the proposed banner was butt-ugly and had no historical significance to the state was beside the point. (The Metropolis piece also talks about this to some extent.)
The reality is that the Mississippi Legislature — particularly the white Democrats who run the place, despite the fact that the Republicans and black Democrats could easily make a power-play if they felt like it — made a shrewd political calculation: they punted on the issue to save their jobs (a reasonable thing to do; realignment hasn't reached the state legislature here yet, but voting for a new flag was one sure-fire way to make sure it did), and they counted on having the popular mandate to not change the flag to insulate them from any backlash from the NAACP and other groups pressuring for change. The only possible downside for the legislature's white Democrats, who really didn't want a new flag anyway, was that if Mississippi's black population had decided to turn out disproportionately in the election, they could have gotten the new flag. In the end, only 30% of the electorate showed up, and the "old" flag won in a number of majority-black counties. Realignment was forestalled, the NAACP went away, and nobody in the state really seemed to care all that much.
Of course, virtually nobody in the state cared much about what anyone outside of the state thought either, which is probably why Mississippi is viewed as little more than a collection of backwater hicks and a source of occasional "local color" for Robert Altman films.