I've been obsessed with reversible clothes for the last year or so. I go fabric shopping flipping all the fabric over to see what's on the other side. Most of the fabric came from Joanns, Nichole Miller has a line of polyester stretchy shiny knits and recently they had some dry-fit type workout stuff also reversible.
I started out with no sleeves because they would be easiest. Most of the time I just use one row of zigzag and one row of straight stitch on a very narrow seam to mimic the look of flat-locking. Edges were serged. One side is silvey the other a light grey but the photo shows less contrast. Also made it V-neck/ scoop for maximum versatility.