Coccidia are host specific or at least genus specific. You won't get them from your dog or your chameleon unless you have a very compromised immune system.
There is a cat or dog parasite that can go thru skin but it's not coccidia. Hookworms? maybe? I'd have to look it up.
Eimeria and Isospora typically require only one host in which to complete their life cycles. Some species of Isospora have facultative intermediate (paratenic or transfer) hosts, and a new genus name, Cystoisospora, has been proposed for these species of Isospora. Coccidia are host-specific, and there is no cross-immunity between species of coccidia.
Source the Merck Veterinary Manual