It's slightly arduous to do the true kind without the specialized machine, though. I usually use a similar seam that's nearly as strong and a lot easier, which looks the same on the outside of the garment.
You'll need regular thread in the bobbin, and two spools of thread in the top of the machine: one regular for the construction stitch, and one of heavier topstitching thread for the decorative topstitching. Note that there's no functional reason not to use the same thread for the topstitching, but the heavier thread looks nicer. In this instructable I've used orange thread in the bobbin, white for the regular thread, and light green for the topstitching, so they are easily distinguished in the pictures.
Step 1: Cross sections
The first pic is a cross section of a true flat felled seam. The second is the cross section of the alternate version (both alternates have identical cross sections). If your sewing machine doesn't like heavy weight fabrics, I recommend the alternates not only because they're easier, but because they produce fewer thicknesses of fabric to sew through.