Here's what you will need: a stamp, an acrylic block or piece of wood, some 3mm or thicker craft foam and/or red rubber, ink and some saran wrap (or cling film-- whatever you choose to call it).
The first step is to make a "sandwich" on top of your acrylic or wooden block. Put the block on the bottom, then put a square of red stamp rubber, then add a square of craft foam (just the cheap kids' craft foam that you can get at Michaels, JoAnn's, etc.). If you don't have any red stamp rubber, I'm guessing that two squares of craft foam would work just as well. The point is to get a sproingy squishy surface.
The next step is to practice your deli skills and wrap this thing up nice and tight with saran wrap (cling film). I didn't use tape or anything; I just wrapped it all the way around so the saran wrap stuck to itself on the back. Make sure that your saran wrap surface on top is wrinkle-free because this is where you'll be stamping your image.
Now you're ready to stamp onto your saran-wrapped surface! I tried several different inks and had the best luck with Ranger Archival ink since it's pretty juicy. You can use other kinds, but the image was lighter and fuzzier with the other inks I tried. Stamp your image onto the saran-wrapped top of your sandwich.
Now treat this as you would a normal stamp: press it down onto your paper. Use those muscles and rock it back and forth slightly for maximum image transfer. And wah-la! Here's how it turned out as I lifted the stamp off my page:
So there you have it! An image flipped the opposite way. And the best part is the clean-up: simply peel off your saran wrap and your rubber/foam squares are good to go for another day.
So how does our flipped image compare to the original? Here's a side-by-side comparison. The one on the left is the one we flipped and the one on the right is the original stamped image.
The one on the left will never be quite as crisp and dark as the original because you're stamping it twice instead of just once: you have to stamp to the saran wrap, then stamp from the saran wrap to the paper. But hey- I thought it was pretty darn good replica if I do say so myself.
There are probably several more genius ways to go about this, but all in all, I was pleased with the results. So if you've desperate to have an image face the other way, look no further than your kids' craft foam collection and your pantry!