One of my favorite creative projects with quilting, is making reverse applique jackets bags and throw quilts. They are very graphic and exciting, and I always do the work in soft comfy fabrics.
it can be done with woven cloth or nonwoven.
For finely woven cloth like the tight-weave "batik", stitch two very tight very close rows of the design, to guard the fabric from pulling out from the stitches. For our "normal" quilting fabric and for flannel, those two tight rows should be a bit farther apart, maybe 1/12th" gap, for more security.
Usually I select felt (Woolfelt from National Nonwovens, which is mostly rayon, and found at JoAnn.com as well as in their stores), but knits are successful too. Using those fabrics I can use a regular stitchlength, and stitch the design one time.
For felt, I use Kid Fiscars scissors for ages 6 and up, and cut a scan 1/8th inch outside the sewn line. This means. I will have created the stitching design a bit skinnier than for quilting.
You can do this with many designs which you find in this website, if you can make an echo pattern inside the design you chose to applique. Select the pattern on your computer screen, select to make an echo, inside, 1/8th gap, 1 row of echo, NO smoothing of the shapes. That echo is the pattern you then save into a catalog of reverse applique designs, so you don't confuse it.
In many cases all you would need to do, instead, is simply make the design a little smaller than you want, without bothering with the echo.
When the project is minkee (see my tutorial on Moose Sunrise), I quilt two layers of minkee facing up, and a third facing down for the backing. I cut wider than 1/8", but not quite as wide as 1/4", and have to use my sharpest scissors, the nap slides under the blades a bit so it is slower to cut than felt. Cut it sitting in a corner with a small vacuum next to you to keep the lint under control.
For using this technique with a knit without the nap, use a bit of common sense, is it a close knit? Then one row of stitching is enough. Is it a loose knit? Doublestitch the design, and leave a gap of 1/12th" between the two stitchings.
If you are looking at this tutorial with no pictures to illustrate, you are seeing it right off my ipad. I will return to it from my desktop in a day or two, to add illustrations for the steps.