I called these pillowcases European style the other day, but I don't know if that is the proper term. I had never seen them until I was gifted a pair from Liberty of London so I figured it might be the style from across the pond rather than American.
I made mine with 3 separate pieces but you could make them with one big long piece if it is going to be all the same fabric. I was working with pieces 2 yards and smaller so I just took measurements from the Liberty cases (which were made from 2 different fabrics) and added 1/2" each way for the shrinkage of the flannel.
It takes about 40" for one pillowcase, or if you want to make 2, it takes 2 yards. When cutting for one you have a left over piece that you can use on a second pillowcase. With the fabric folded as it is when you buy it, I cut 1 piece 29.5" long and 1 piece 10" long. Then I turned the pieces and cut a tiny sliver off the fold edge and 1/4" off the selvage edge. This gives me 2 pcs. 29.5" long. Also you will have one piece of 10" left over.
Step 1 - Hem one short side of a 29.5" piece with a 1.25" hem
Step 2 - Hem the 10" piece on one long edge with a narrow hem
Step 3 - Layer the 2 - 29.5" pieces with the unhemmed one on the bottom, matching all raw edges on 3 sides.
Step 4 - Place the 10" piece on top of the end with the 1.25" hem matching raw edges on 3 sides. Pin as much as you want. 
Step 5 - Sew all around with a serger or with straight stitch and then come back and zig zag the raw edges.
This is what a serged stitch looks like.
Step 6 - Turn the 10" piece right side out. this is that the finished end looks like.
Step 7 - Turn the whole pillowcase right side out. this is what the finished back view looks like.
When your pillow is inserted and the end of the pillow tucked under the 10" piece, you have a case that is just the size of the pillow without any open extra flaps like a regular pillowcase.
You can see here what happens with a one way print (or directional of any kind) so if this bothers you, make sure you choose an allover print.
I made mine with 3 separate pieces but you could make them with one big long piece if it is going to be all the same fabric. I was working with pieces 2 yards and smaller so I just took measurements from the Liberty cases (which were made from 2 different fabrics) and added 1/2" each way for the shrinkage of the flannel.
It takes about 40" for one pillowcase, or if you want to make 2, it takes 2 yards. When cutting for one you have a left over piece that you can use on a second pillowcase. With the fabric folded as it is when you buy it, I cut 1 piece 29.5" long and 1 piece 10" long. Then I turned the pieces and cut a tiny sliver off the fold edge and 1/4" off the selvage edge. This gives me 2 pcs. 29.5" long. Also you will have one piece of 10" left over.
Step 1 - Hem one short side of a 29.5" piece with a 1.25" hem
Step 2 - Hem the 10" piece on one long edge with a narrow hem
Step 3 - Layer the 2 - 29.5" pieces with the unhemmed one on the bottom, matching all raw edges on 3 sides.
Step 4 - Place the 10" piece on top of the end with the 1.25" hem matching raw edges on 3 sides. Pin as much as you want. Step 5 - Sew all around with a serger or with straight stitch and then come back and zig zag the raw edges.This is what a serged stitch looks like.Step 6 - Turn the 10" piece right side out. this is that the finished end looks like.Step 7 - Turn the whole pillowcase right side out. this is what the finished back view looks like.When your pillow is inserted and the end of the pillow tucked under the 10" piece, you have a case that is just the size of the pillow without any open extra flaps like a regular pillowcase.You can see here what happens with a one way print (or directional of any kind) so if this bothers you, make sure you choose an allover print.