Accurately shooting a slingshot or ANY 'primitive' weapon not only takes practice, but also proper 'form.' One thing I have found that most people with accuracy problems have in common is the lack of a proper ANCHOR POINT! You need to pull a slingshot or bow back to the same anchor point for EVERY shot!
When shooting bows I anchor my MIDDLE FINGER in the corner of my mouth.
When shooting slingshots I anchor my THUMB in the corner of the mouth.
I shoot purely instinctively, this means practice is mandatory, esp. early on with a new setup in order to 'reprogram' the brain and muscle interaction. The first time I learned to properly shoot a 56# recurve bow instinctively, I shot DAILY for over a month and was able to CONSISTENTLY put every shot into the vital area of an ELK out to 40yds by the end.
When shooting instinctively, be sure to CONCENTRATE on the smallest possible spot you can see, burn a hole through it! Draw your weapon back to your anchor point and 'feel'/'see' the projectile go to your spot in your mind. The release will take place 'naturally', don't force it, 'will' it.

This is the 'essence' of instictive shooting.
If you think about how to shoot instinctively, it is like throwing a ball or pointing your finger at something. You just 'do it.' There is no conscious effort to 'aim' the brain acts as a ballistic computer and does faster than you can actively think about it. Hence the practice involved to 'reprogram' your computer to what 'feels right!'
The basics:
Concentrate on a spot!
Get a solid and consistent anchor.
The support arm should be solid, it is what actually adjusts for elevation and windage without being looked at or thought about.
Use your BACK MUSCLES! Don't try to muscle the weapons with your arms. Squeeze your shoulder blades together, even with slingshots!
Good luck!