I am of the opinion that these birds do not exist.
Prove me wrong, someone please!
I have never heard of crossing a chicken and coturnix, that sounds just as unlikely. BUT... you can cross a chicken with a guinea, a guinea with a peacock so it's hard to draw the line at what's impossible and what's not. I had a button rooster than mounted his coturnix hen all the time and I tried hatching some eggs from that but it didnt work, I also tried AI from coturnix roos to buttons and that didn't work either..