There are a few ways of Reducing Runout of a 3 jaw chuck. One way is to fit a better quality 3 jaw chuck that fundamentally has less runout. This was what I did when I upgraded the standard 3 jaw chuck on the Warco WM240b to a Soba chuck.
You can use shims to adjust the grip on particular jaws, this requires the use of a dial gauge. At this level it actually feels like it’s worth jumping to an independent 4 jaw chuck.
Re-grinding the jaws is an option, just be careful to protect the lathe bed.
A simple method is to mark the workpiece and one of the jaws.
This doesn’t reduce the runout, but it allows you to remove the workpiece for an operation and return it to the same orientation. You can also rotate the workpiece to machine the other end and get a good alignment to both faces. The is a simple way of reducing runout of a 3 jaw chuck when machining stock material.
It is best to use a permanent marker and if you’re using cutting fluid you might need to re-apply marks. If the workpiece is a small diameter then best to use a finer marker and mark the material along it’s axis. If the line wanders then it is not so useful.
This technique works even for the best aligned chucks with the smallest of runouts. Rather than just taking my word for it, try the technique on an offcut and just machine the diameter slightly smaller, rotate and repeat. Then see how small the step in diameter is between the two faces.