• Cut your three squares (two of the flannel, one of the felt)

Stack these three squares on top of one another IN THIS ORDER from bottom up:

• Pin your fabric sandwich in place and begin sewing around the edges with a ~¼" seam allowance.  
• One one side of the square, you'll want to leave a gap to allow you to flip the coaster right side out.  I suggest leaving about 2 ½" in the middle of one side (not on a corner).  The white dashes in the picture above are highlighting where you should sew.  
• Be sure to backstitch both ends of your gap.
• Next, trim any excess fabric from around your seam.  When you're trimming, however, try to leave more fabric around the gap ... since you'll be tucking this inside and top stitching to close gap.
• One more tip when trimming ... leave the flannel fabric around the gap (like I just described above), but trim the felt down as shown (so the gap doesn't get bulky when you top stitch it closed).
• Next, we'll be flipping the coasters right-side-out.  To do this, open up the coaster at the gap ... between the two flannel pieces.
• Flip it right side out!
• If you flipped correctly, the felt should be tucked inside and there should be a little extra fabric at the gap.
• Tuck that extra fabric into the gap as shown and iron in place.
• To finish (and to close that gap), simply top stitch around the coaster on all four sides.  Here's where you can choose a contrasting thread color for fun.