Anything other than toilet paper, which is designed to disintegrate completely in water, should not be flushed. That includes facial tissue, paper towels, and cleansing wipes. If you have modern, smooth PVC waste pipes you might get away with it but the water treatment plant won't like it.

If you have older clay or cast iron waste pipes, feel free to take your chances as GP says. I'd rather not deal with overflows and I'd rather keep my money than give it to a plumber to snake out a clogged drain line.

Let's put it this way, are any of these "flushable" wipe companies willing to insure you against plumbing costs and damages caused by their wipes?