3 jaws are quick to set up and almost on centre. Never remove work from it until it’s finished or as you found out it won’t grip in the same position
a 4 jaw would have been much worse as gripping hexogon material in it is not easy to set true, even worse if it has to be removed and later re machined.
If your flywheel was correctly secured in the chuck, drilling. AND. Reaming the bore should leave it without wobble, but probably a faceplate job to get it really true
i can’t exactly understand why you use hexogan fir the axel , how and when does it wobble, with the hex in the lathe chuck or when the flywheel is mounted in the engine?
the axel would probably have been better turned between centres or as a minimum with a large overhang and tailstock support
do a test. Grip a bit of round stock in the 3 jaw, and use a dti to determine the runout. If it is more than sat 5 thou, remove the chuck from the backplate skim a 1/16” off the register. Re mount the chuck and tap it with a soft hammer to get the bar to run true. Mine will grip to 2 thou on all diameters after this treatment, and it’s a cheap polish chuck