I don't have any experience evacuating over long distances from a disaster, but I have done some long distance hiking in my youth. So comparing this survival with my experience and knowledge of thru-hiking and this is what you get:

Statistically, people starting the Appalachian trail, without prior training, is 9.5 miles per day, while a hiker that has rigorously trained will average 12.8 MPD. The top average after a month on the trail for both groups was 16 MPD, but the conditioned hikers hit this peak earlier. A good reference for this is Long-Distance Hiking: Lessons from the Appalachian Trail by Roland Mueser.

So a conservative estimate would put 400 miles at around 35 days. Weight loss is inevitable, and probably beneficial for most of us (certainly for me). But lack of adequate supplies of protien and fat over time will lead to strength and endurance loss, impaired critical thinking and higher risk for injuries. Carbs, sugar and endorphins can only take you so far. Most male AT hikers lose both fat and muscle mass during their hike due to insufficient food intake.

I would never rely on MRE's for bug-out food supplies. The caloric value doesn't balance out the weight and bulk problems. Lightweight, high-value foods such as jerky, air-cured sausages, nuts, oatmeal, beans, brown rice, whole-wheat pasta and hard cheeses are typical fare for thru-hikers and would work just as well in long-distance bug-out hike. Peanut butter, Nutella and chocolate are also popular hiking foods (though I question the value of chocolate). Most thru-hikers (including myself) budget around 1.5 lbs of food per day per person, but many claim that 1 lb is enough. Even thru-hikers don't carry more than 10 days of food due to size and weight concerns.

At my age and current condition, the possibility of traveling 400 miles by foot is unrealistic without outside assistance. Fortunately, I don't live in an area where I believe my threat types and damage radius extends that far that rapidly. So my survival plans are more focused on shelter-in-place and/or traveling more achievable distances, preferably in or on a motor vehicle, which doesn't necessarily require pavement. This presents two advantages: lower caloric needs to support lower activity levels and better cargo carrying abilities. Of course there are other potential risks with this plan. Hopefully the church and Boy Scouts will be there if my plans don't work out. ;-)