Should you do stretching before walking or walking and stretching?
What do you mean by warming up? How do you warm up?
One of the first things you want to do before you do any type of exercise including walking is to stretch your muscles for at least 5 - 10 minutes. This will reduce stress and strain on the muscles that you are working and they won't be as tense if you didn't stretch first.
Warming up is doing a light to moderate walk to increase the heartrate. The higher the heartrate is increased, the more blood will be pumped through your body which carries oxygen.
Most sources on stretching I've read all agree that stretching cold muscles (i.e. pre-warmup/exercise) isn't good.
I personally believe focused (5-10 minutes) stretching works best at the end of a workout, but if you want to stretch before a workout I would do 5-10 minutes of warmup (if you're walking just start walking) and then do some light stretching before moving to the main portion of your workout (weights, the rest of your walk whatever).
I like to do more dynamic stretches at the end of my warm-up (shoulder mobility with a stick, swinging legs forward and back, side-to-side), and the more static stretches (calves, hammies etc) at the end of the workout.
Based on the information you have in this question (not sure if it is inspired by another), there is little benefit to stretching before you start your walk. Walking in and of itself doesn't present a tremendous load on the body or cardiovascular system. The range of motion is not greater than what you currently need for regular life. In short, stretching to prepare for walking will not provide you any value whether you are warmed up or not.
When your muscles are not prepared to work, a sudden increase in effort can cause injury. Essentially, the muscles and tendons are not pliable and if you are asking for a larger range of motion and/or the addition of more weight your muscles can revolt by cramping up. In some more extreme cases where there is load on your back, it can cause the spine to flex more than it is designed to.
To solve this problem, you have to prepare your muscles to get ready for work. Part of the process is to get blood flowing through your muscles, which is done by increasing your heart rate. A brisk walk can do that for you. In some cases you need to prepare for a greater range of motion while protecting your back such as with weightlifting. In this case, performing the motion of the technique without any load on the bar will accomplish the same thing while improving your range of motion for the work you are about to do.
If you are going to put forth a much greater effort, you need to ramp up your warmup. For example, if your intent is to run quarters (sprinting from one end to the other of a basketball court 16 times) you might start the warmup with a jog around the court. Then do a couple slow sprints to get the feel for the main part of the work out.
Walking itself is a warmup. You don't want to stretch with cold muscles, as that rarely gives you what you want. After you warmup, then you can stretch. Track and field athletes will run a lap or two to get ready, then perform the stretching they need so they can have the full range of motion they want while doing their main work. They will do a more rigorous stretch after the workout as part of their "cooldown" routine.
To answer your question directly: walk first, stretch after your muscles are warm. If your goal is greater flexibility and range of motion than you currently have, save the bulk of your stretches till after you walk.
You didn't ask, but I'll include it anyway:
After you've done the meat of your exercise, it's a good idea to bring your heart rate back to normal and your muscles back to a resting state gradually. Many exercises are anaerobic (sprinting, weight lifting, most sports), and as a result you may have built up some lactic acid in your muscles. That's part of how muscles get energy during anaerobic activity. The cool down process helps the blood keep flowing to flush the excess lactic acid without adding more.
Runners will cool down by decreasing their pace gradually, at least until their heart rate is well in the aerobic zone (you'll be able to talk in sentences). Many athletes will use a more full stretching routine to increase their range of motion and help them perform their technique better by the next workout.
The answer I gave is the basic structure of how I exercise. First, I warm up doing some lighter load lifting (since I lift weights) until I get to my work weight. Next, I do the exercises I set out to do. Finally, I cool down by stretching to improve my range of motion. This basic structure works for me, and it will work for anyone regardless of the type of exercise they do. The type of work that you use to warm up or cool down really depends on the main exercise you want to do.