Would an arm sling be something to consider after my next revision surgery to really ensure minimal stretching and movement?

It's not clear for what clinical reason you're having a revision. Regardless I can't think of a situation where the operative outcome would be benefited by use of an arm sling.

I have never heard of any one using arm slings for the reasons you describe.  You should be able to use your arms freely after surgery but with limited exertion for several weeks. Best to review preop plans with your surgeon.

While each surgeon has his or her guidelines for postoperative care, an arm sling is not something I have recommended post breast augmentation. Consult in person with 3 experienced and expert board certified plastic surgeons to review your experience and understand your options.

You did not specify the nature of your complication or the reason for or type of revision that you had, however, I doubt that hypermobility of your joints had anything to do with it.  You might have done too much during your recovery, but that is a different matter.  I would not encourage you to wear a sling postop, just on general principle, as I have never in my career felt the need to have a patient do this (and I have operated on professional female athletes even), and I would be concerned about the risks of stiffness and frozen shoulder that could result from wearing a sling.  You would do better to wear a supportive bra and strap and follow the activity recommendations of your surgeon to a "T."  One other thing to consider, weird and unusual as it is, is the possibility for a genetic "elastosis" condition which may affect the strength of the collagen and elastic fibers in your tissues.   Many flexible people have such conditions, Ehlers-Danlos Syndrome being one of the better known (and think of the "Indian rubber man" at the circus), and these things will affect how your tissues tolerate the stress of implants.  Ask your family doctor and members of your family about this, just in the way of closing the loop, but if there is any reason to do a formal medical work-up on you for one of these conditions, it would be beneficial to answer the question, because on the outside chance that you have one of these conditions, it could predispose you to recurrent problems with implant displacement.  Good luck.