Is this allowed? What would it look like mechanically?
So, that sounds like fun, but is it realistic to play "baseball" with slingstones?
TL;DR - Nope
There are a lot of factors that might be reasonable about it, but there is one big problem: a baseball batter only needs to hit a ball pitched into a specific strike zone. The kobolds won't be aiming for the strike zone, they'll be aiming for him.
Below is detailed analysis comparing slingshot with "big league" baseball.
A major league baseball fastball goes about 42 m/s (95 MPH) or more. Slinging.org reports that leaden slingshot (that is, the high-quality kind, better than rocks or baked clay) can be thrown at a speed of up to 33 m/s (78 MPH) from a classical Egyptian sling - that's the speed of a major league changeup. So the slingshot is actually in the lower range of major league baseball pitch speed, a speed not too fast to be hit.
A typical slingshot weighs 40-160 g (1.4-5.6 oz), while a standard U.S. baseball must be within 142 and 148 g (5 and 5 1/4) ounces. So the weight range is also comparable. So the club could deflect the slingshot - it wouldn't be like trying to bat away a bowling ball.
A baseball is 72.64–74.68 mm (2 7/8 – 2 5/16 inches) in diameter while a large-end slingshot would be about 39 x 22 x 16mm (1 1/2 x 7/8 x 5/8 inches).
Since the slingstone is roughly half the size of the baseball, it would clearly be harder to hit.
The strike zone
It's time to finally bring up a very important factor. A baseball pitcher is (usually) not trying to hit the player with the ball. A baseball batter only needs to hit pitches in the strike zone while our slingstone batter would need to dodge out of the way of a well-aimed shot and then hit it.
Some of the stones would be coming in higher or lower than the strike zone where they would be more difficult to hit--such as at the target's head.
Any baseball fan could tell you that if a pitch, even an changeup, is coming at a batter's head, he tries to get out of the way of the pitch. He doesn't try to hit it.
So, is it reasonable?
If the slingshot is heading for the target (that is, the hit roll was successful) and the slinger is standing comparably as far away as a baseball pitcher (that is, around 60 feet), then any baseball fan can tell you that even a superstar cannot bat the incoming projectiles away.
Unless you are willing to consider your hero PC's to be greatly more athletic than major league baseball players who train to do a similar thing, batting away slingshot is not plausible.
If your campaign emphasizes a gritty realism, then there is no reason to extend the rules to make this feasible.
Applying what we know about baseball, an attempt to bat away a slingshot directed at you should have a very high DC.
As baseball pitchers rarely have trouble hitting a batter when they choose to, granting the attackers advantage on hitting the loon might be appropriate as well, as he is has stated he's just standing out there in the open with his club.