Warmup
We intuitively know not to start throwing a ball or stone with force without first warming up our arm/shoulder. Slinging is very much the same. We are not sure why but there seems to be a disconnect on this principle and we see many people try to give the sling a powerful first throw. We think it has to do with the concept that people tend to think that the sling is the throwing force. Nope, it's still your arm.
Try to resist the urge to pick up a sling and give it a solid first throw. Start with whatever warm-up technique works for you. We like to warm up with some shoulder circles, arm circles (both directions), and some triceps stretches. We end the warm-up by lightly throwing 20-30 small stones or tennis balls by hand, depending on location.
We also like to warm up on our target. Meaning that we like to take a few low-power practice shots at the target. This helps to continue the arm warm-up but it also helps us correctly judge the throwing area and target before we launch into our regular throwing cadence.
If it has been a while since you have regularly used your throwing muscles/mechanics, take extra time warming up and limit your slinging sessions to end well before fatigue. It won't take long for your throwing endurance to increase, as well as gain some added pep to your throws. But allow your body to dictate that timeline or a strain is very likely.
These warm-up steps may seem extensive or overdone but it does not take long and the prep is worth the investment both in terms of avoiding injury or rashly misjudging the target. Remember, the sling is a powerful tool and it more than deserves the added precautions.
Interestingly, you will probably find that the sling will allow for longer periods of powerful throws than just throwing by hand. Our guess is that has to do with the fact that we usually don't max our throwing limits while slinging like we tend to do when throwing.