I want to experiment with backend changes that are exposed in equal percentage buckets within different cohorts (similar to the above question). Based on the above discussion it seems that the best way to do this is to create a feature flag, create experiments with targeting conditions and add all of my experiments to the same feature flag and then send all of my users to this feature to get their assignment value? Would this ensure that each experiment has the same population split percentage wise but not necessarily in terms of overall number?

Are all of your cohorts mutually exclusive, meaning that a member of cohort a won't appear in cohort b?

Yes, that would be the goal in terms of the setup. If a member is in cohort A they should not be in B

Yep, then this should work!