If the current patio is in good shape how about acid stain. You could draw the flagstone shapes, stain each one a different shade. Acid Stain sounds nasty but gives quite a nice look. Just be sure and read the instructions first.
Paws

Some friends of mine back in IN did what you're suggesting and love it. They had their concrete entryway done over with the overlay to look like brick and it's incredible.

We have an old concrete patio that we're going to redo (one of these years) in the overlay, using a stone finish. We thought about putting a layer of decking on but the look doesn't match our yard and it's too thick. The overlay is not very thick -- I don't remember specs but I can't imagine it would be much thicker than flagstone. We only have a few inches clearance between our current patio and the door sill and that's plenty of room for the new surface.

I've seen samples of the product and it looks incredible, and care is supposed to be a dream. I'd be interested to hear if anyone has any bad experiences with this. See link for photos but I can assure you the finished product looks much better than the photos can show. In case you can't tell, I'm hooked on this idea :)

Here is a link that might be useful: concrete overlay

I would ask an experienced contractor in your zone about wwhat would work. I would be concerned in colder winter areas that the new top layer might crack on you.