Best burger is probably Bulldog Burger in Ridgeland. I've been to Lou's and I was very underwhelmed (although it has a lot of hype).
CS's is more about nostalgia than the actual burger. For more nostalgia, try Beatty Street in Jxn (my favorite). Both of these plus Stamps (and really Lou's) are really not easy to get to from Flowood (assuming you are near the Old Fannin Rd area and wanting to wrap lunch up in a hour).
Mugshots and Burgers and Blues are both good, but Bulldog Burger is better.
The burger at A'ha Donuts in Purl gets a lot of recommendations, but I haven't tried it (again it's not easy to get to from Flowood).