Chrome does give access to localStorage/sessionStorage in Incognito and this can be used to communicate between tabs on the same domain, but just like cookies and cache this data is wiped if you close the Incognito instance.
It's certainly a mystery, because you'd expect any capability fingerprinting (some combo of UA, extensions, CPU/GPU specs, IP etc) to give an identical result between profiles, so it does seem there's some per-profile difference. But I can't think of any browser API that exposes something like an ID...
