Is it possible? Has been done already. Advisable? Depends, it does work for SOME systems. A few things to consider. Do you already have materials for a 6" chimney system? How much area do you intend to heat? Insulation values of said living space? Climate? Most importantly, do you need the full output an 8" system is capable of? I.e. a properly built 8" rocket combustion unit, running "half throttled" into less than optimal length of mass ducting, can run fairly well into a GOOD 6" chimney system (Good as in a straight vertical chimney that drafts strongly all year round, including windy and stormy conditions).
With only 12 feet of 8" pipe snaking through your mass, a little extra dwell time for the hot gases to heat the mass, as afforded by a smaller chimney, may turn out to be an advantage. 12 feet of pipe in the mass is really short for an 8" system, but how many elbows? Those need to be considered also, since each 90°elbow equates to about 5 feet of straight pipe. The exit elbow that turns vertically to the chimney is not counted.
Keep in mind that an 8"
RMH into a 6" chimney is experimental territory. If buying a new chimney I'd be inclined to bite the bullet and go 8" all the way. But if a 6" chimney were available for very little cost, the experimenter in me would probably give it a try.