6-iron tee height.
¼ inch ball-bottom. Same as the 5-iron.
The short answer
¼ inch (6.4 mm) ball-bottom, the same as the 5-iron. Use the lowest tee in the pack.
Consistency is the point
There is no separate 6-iron tee height, and that is deliberate. Every mid-iron through the bag should be struck the same way: ball first, ground second, low point ahead of the ball. If you change the tee height between clubs you are changing the lie, and a changing lie is exactly the variable that makes range numbers untrustworthy.
Set the same quarter inch for the 5, 6 and 7 iron and the only thing that differs between those shots is the club in your hands. That is what a practice session is supposed to isolate.
The 6-iron gapping problem
Most amateurs have a distance gap that opens somewhere around the 6-iron, where the club gets long enough that strike quality falls off. If you are teeing the 6-iron higher than the 7-iron without realising it, that gap will look larger in your data than it is in reality, and you may end up re-gapping a set to solve a problem the tee created.
Why not flush
Flush works on grass, where the turf absorbs a slightly heavy strike and tells you honestly that it happened. On a mat the rubber underlayer bounces the sole into the ball instead. The strike reads as acceptable when it was not. A quarter inch keeps the ball just clear of that failure mode without turning the shot into something you could never play off the fairway.
What too high looks like on a 6-iron
Ballooning. Launch angle climbs, spin drops, and the ball climbs steeply and lands short of where the club should carry it. If your 6-iron numbers on a simulator look higher and shorter than they do outdoors, the tee is the first thing to check, before the swing.
Setting it
Whatever tee you use, the requirement is that it returns to the same height on every swing. A wooden tee pushed into a mat hole and a rubber tee compressed under the mat both drift. If the height moves, the data moves with it, and a session you meant to compare week over week stops being comparable.
Should a 6-iron be teed lower than a 5-iron?
No. Use the same quarter inch of ball-bottom for both. Keeping the lie identical across mid-irons is what makes the distance gaps between them meaningful.
Why does my 6-iron fly higher and shorter indoors?
A tee that is too high is the most common cause. It adds dynamic loft and reduces spin, which produces a steep, short ball flight.