If you can dodge a slingstone, you can dodge a ball. 

During the Indian Wars on the Great Plains and later during the Spanish American War, the rifle the US were using were launching a one ounce projectile (30g) at 1300 FPS (400MPS).  The Indians and the Cuban troops would duck when they saw the flash and the puff of smoke.  If the trooper was aiming at the guy, he would now miss.  That was good out to about 100 yards or meters, they would then rush in while the trooper was reloading.  That was also true in the Philippines.  Brits had the same problems in Africa fighting with their Martinis'.

So, if a guy can dodge when he sees a bullet being fired at him, (Note that the shootee is not actually dodging the bullet, he's just moving out of the area he was in) I see no reason that someone couldn't move a pace or two when he sees a slinger release to cause a miss.

BTW, both rifles shot a bullet about the size of the first joint of your thumb.  And I haven't read any accounts of anyone being able to see the rounds coming in.  Also, FWIW, you can see a tracer round coming but you don't have enough time to dodge.  So, if you put some sort of light source on a gland, you would be able to see it coming.  I have no clue if you would be fast enough to get out of the way. 

The .25 second reaction time is from resting or neutral, if you are expecting it, your reaction time is faster. Otherwise, if you are in a boxing match, where the travel of a punch is a lot quicker than a .25 seconds, the fight would be one punch and over.  No blocking, no bobbing and weaving, whoever punched first would connect. By the time the other guy reacted, he would be hit.  And the fight would be over.

I think it's possible, if you train to do it you could get pretty good.

Polynesians trained to dodge and deflect multiple spears with their hands. Up to 9 spears could be thrown simultaneously at the experts (no idea if that is true). But they never used shields in war.

My boys throw tennis balls at each other, but not as hard as a man could. I started their training by having them behind a chainlink fence with a layer of coco wire in front of it and throwing full force with balls. Once they got used to it, they don't flinch. If they keep going eventually they'll be like boxers. Boxers do not move away from a punch or flurry, they just move the portion of their body that's in the way.

Lacrosse players are probably the closest to needing no other training. Any martial art should have offence and defence taught if you think of slinging as a martial art.

I agree, seeing the person slinging at you is a very important factor for a successful dodge. If we talk dodging by means of seeing the projectile only (not the slinger), then it becomes much much harder. With woods as a backdrop, you often cannot see dark or dirty stones coming towards you as they blend in with it. No doubt some slingers painted their projectiles for this effect. It also depends on the size of the rock and whether it's smooth or jagged. A big, slow, buzzing, rock will naturally give you the best chance. Small, elongated stones travelling 60+m/s? Best of luck to you, I say.

Define dodge. What Bill mentioned is technically dodging even if you can’t see the projectile. The other dodge would be seeing and responding intelligently before it hits. Anything that exceeds a human’s flicker fusion threshold is going to be pretty hard to dodge intelligently seeing as you cant see it. Velocity, lighting, size of stone etc all will play a part.

So, yes you can always dodge, no you can’t always dodge out of the way (since you can’t always see it) but evasive action could be taken one way or another even if that evasive action mistakenly brings you into the path of the stone as opposed to out of it.

However at 20-25 meters with a hard throw coming at you, expect to be sore the next day.