Linen will definitely have a tendency to fray more than a lot of other fabrics (since it is more loosely woven). Here are a few things that will help prevent the fraying from spreading too far:
-Leave yourself a fairly large seam allowance. At least 5/8", in my opinion. The more fabric in the seam, the more it would have to fray to get through.
-Zig-zag the edges with a fairly small stitch length. If the zigzag is too large, the fabric will still fray in between the v's.
-Double stitch all of your seams (and for kids clothes, I actually triple stitch, since they will get so much wear and tear!). Use a pretty small stitch length ... this will give the fabric very little room to be able to unravel since two layers of tight stitching will be holding everything in place.
Good luck!

Jennifer