You can buy sheets of laminate, which you could use to protect photos as well, or you can use fixative made for pastels and other types of artwork. If you want your flat cat to last awhile, I'd try the laminate. Personally I haven't used it before, so I can't say how well it works. My advice is to take a sheet of paper, scribble it with pastels and give it a try. I can't think of why it wouldn't work and next time, I plan to use this method.
Laminate comes in different thicknesses and you only need a thin one to protect, so a 1 mil thickness would be ok. If you can find a 5 or 10 mil, it might be thick enough to skip mounting the flat cat to cardboard. I looked around and here is a link to laminate sheets. Since it can be rolled, it must be the 1 mil laminate.
The adhesive and fixative I used.
I am not advocating any brands, just letting you see what they look like.
They are available at any arts & craft or art supply store.
There are 2 types of fixative, workable and final. You want to use a final fixative. As the names imply, you can continue coloring with a workable fixative but once the final fixative is applied, that's it, you're done. Spread newspapers out and use in a well ventilated are. I do it outside. This stuff is dangerous, so follow the precautions. Apply light coats, allow to dry between applications. Unfortunately, the fixative will change your colors, mostly darkening the light areas, so that may be another reason to use a laminate.
If you look online, some people will tell you hairspray works as a final fixative. NEVER USE HAIRSPRAY! Hairspray has conditioners and oils in it that can blot and leave oil stains on your flat cat. What a shame to put in all that time just to ruin it after you've finished. Fixatives cost about the same as hairspray. I have no idea why someone would do such a thing, maybe they don't care about quality or they think they are saving money. Fixatives are specially formulated to spray evenly and are oil free.
The next step is to spray the back of your cat with adhesive and attach it to cardboard. You could use poster board but don't use the cardboard with flutes in the middle. They crush easily as does Foamcore. There's a better grade of Foamcore called Gatorboard. Gatorboard doesn't leave marks if a sharp edge or fingernail rubs against it like Foamcore does. I personally don't care for either and think they are too thick. I used the inside of a postal service mailing box. (Hey, it was free, so the price was right!)
Again, follow the directions on the adhesive, and the same precautions apply. I do this step outside too, spreading plenty of newspaper around. I put another piece of cardboard over my cat when pressing down to adhere it to the board, just to spread the pressure around and protect the art.
Once the adhesive is dry, cut your cat out using an X-Acto knife, a box cutter or scissors. Color the cut edges with a black Sharpie, and attach a stand. You can buy single or double wing easel back stands, but you could make a stand as well. Here's link to a stand: http://www.officedepot.com/a/products/152217/ArtSkills-Easel-Backs-10-White-Pack/
That's it, you're done! I've love to know if anyone makes a Flat Cat. It's a big project if you are drawing your cats, but you can put their personalities into it by emphasizing or de-emphasizing characteristics, unlike a photo. So, good luck, may the spirit of Techne be with you and guide you. Thanks for staying with me during all these posts!
Unless there are specific areas you would like me to address, or a type of cat colored, this will be it. Purrs!