TooManyTools
I've taken hundreds of long walks-runs-biking tours (ranging 20-70 miles); under a variety of circumstances (broken foot, sprained ankle, extended periods of starvation, flu with high fever, etc.; weather from -25 degrees F to 100 degrees F; daylong rainstorms in the 50's (F), blizzards; floods deep enough to submerge cars (plowing straight through on bike), swamps (even on bike), 4 ft. deep snow (plowing miles straight through on foot), extended distances next to and even IN one of the great lakes; from a few hours to 24 hours or more including overnight stays outside); and have never found at any of these time the need to bring along anything.
In the worst case, if you don't know that there will be any water for at least every 20-30 miles (15-20 is where things start getting a little uncomfortable), then the general rule I've found is a gallon or 4 liters a day; or every 50 miles or so, depending on which happens first. Food is not necessary for a week or so; I've done 30 miles each on 2 consecutive days, 20 pounds underweight, in the same weather as New Orleans, without having had much of any food for a week. The only real effect is that it slows down the speed by around 25% and decreases the intervals between water stops.
Shelter is not necessary; rain has no effect as long as you're moving, even down to 40 (F); and temperatures down to 30 (F) don't have much effect as long as you're moving (I've done 15 in 30-35 in little more than a T-shirt and light nylon pants). A nylon spring coat (with a hood) will do down to around 5-10 (F), as long as you're moving. I'll normally wear 2 layers of clothes, long pants and (usually) long sleeve shirt, regardless of the weather or time of year, 0-100 degrees (F); short sleeves if I expect to be around people and it's 80 or above (for reasons of propriety, not comfort; it's better to have long-sleeve shirts because the sun is so damned hot, even in the winter this past year).
For the long-haul, 3 changes of light clothes (preferrably nylon), with 2 on your body (or maybe all 3), rotating them once each day, might be the way to go; or otherwise a small pack to put them in until you find a clean river (or gas station bathroom or other bathroom) to wash them in.
Baton Rouge is only 80 miles from New Orleans, which is 2 day's walk, if only you just keep walking. There were areas directly to the west which were much closer (maybe 20-40 miles) which were nowhere near as affected by the storm. The storm, itself, was only coming in at 10 MPH or so, which is very nearly slow enough to outrun and provided plenty of time to get out of its path.
There is an interesting mathematical and physics problem underlying this: find the route that maximizes the minimum distance between you and an approaching source of danger. The approximate solution is to take the ratio of your speed and that of the approaching danger (e.g. 10:4 if you're walking 4 MPH) and the arccotangent of the ratio (around 60 degrees or so, here). The optimal route is about 60 degrees from the projected route (northward) of the storm -- which would mean, west-northwest. The western end of the storm is blowing south, since it's the northern hemisphere, so the danger of a sea surge is nil; and it was already known the eye was going to miss the city, pbutting to its east.
That would have meant, maybe state highway 61, maybe out as far as Mcelroy (50 miles) before stopping over and maybe turning back after a day or two to help out with the cleanup.
It might have also been possible to hole up in New Orleans University, even though it is on the lake, since most of it remained dry after the flood. For the most part, the flood zone also stopped abruptly at the Jefferson parish boundary, which was only a couple miles (i.e. a 30-60 minute walk) from downtown New Orleans or ... in the worst case ... 3 hours. I've literally crawled 6 miles over 6 hours along the shore of one of the great lakes, including 3 miles and around 3 hours in the lake itself.
