Mike,
Much depends on the knurling tooling you have. If you have a ‘push on’ type of knurl then it will be hard work. Stainless steel of most grades readily work hardens and this form of knurling depends on the strength of the lathe to be able to deform the workpiece sufficiently before it is too hard to work.
The other form with opposed knurls works by loosely clamping the workpiece without the need to force it into contact as above. The clamping clearance can be adjusted as the knurl forms.
Use plenty of coolant to wash away chips that will otherwise become embedded, run the job slowly, as low as 30-40 rpm and work the knurl backwards and forwards along the job as it goes to chase the knurl rather than concentrate effort in one area.
Brush the job with a stainless brush when done to soften the raised points a little and remove any loose chips and dust
Try 316 rather than 304 as a first attempt
Regards Brian