If you have a mill that is worn, this will not work. Even on a new mill, you might get this if not more slop. Just depends on the manufacture and how they set the gib to for the knee and vertical column. You don't want it too tight, doing so the knee will "jump" when lowered. Too loose, the knee will move around on you when it is locked down. But you have to have some clearance left for oil for the knee and get it to travel up and down smoothly when new. Bigger the mill, the more clearance that has to be allowed when fitting/adjusting the two components. There are many ways of obtaining adjustment, the above is one way. My way, for the vertical slide portion of the knee, is to lubricate the slide and gib, assemble, snug the gib. Crank the knee up and down, without movement or just a little, a few thousandths. Re-snug the gib screw, try again. at this point, the knee should be tight, but should still move. Next, back off the gib screw a quarter turn, lock in the gib screw. This should give you the necessary clearance for this slide to operate properly with lubrication.
There's no way to eliminate all of the movement on the vertical slide using a dial indicator as mentioned above. In fact, this may indicate how much wear there is in the slide. So you have to be careful with your measurements and how to read them to determine of it is wear or if it is a correct adjustment for the vertical slide. Feeler gages can be your best buddy on checking clearances on slides too. An .001" feeler is my "go to" when checking slides for wear. Ken