There is one flight-tested engine that uses the design you're suggesting: the Blue Origin BE-3. It is a liguid hydrogen/liguid oxygen fueled engine that produces 110,000 lbf of thrust (throttleable to 20,000 lbf). It powers the New Shepard suborbital launch vehicle, which was first flown on April 29, 2015, and then contributed in the first ever soft vertical landing of a rocket returning from space on November 23, 2015. It is also being considered for use on the ACES upper stage for ULA's Vulcan rocket.
From Blue Origin's website:
The BE-3 is the first tapoff engine to fly. We’ve designed a simple rocket engine, where hot gasses from combustion are tapped from the main combustion chambers and fed back to spin the turbopumps in flight. Having only one combustion chamber with a single ignition event enhances reliability.
I have no information on how they achieved this, as the high temperatures of the gasses in a combustion chamber (6,000+ºF) make it a challenge, like other people have mentioned here. Blue Origin is a notoriously secretive company and hardly releases any information about their operations, let alone information about the design of their engine.