My gut sense is that we're blending audit "types" (for lack of a better word). There is a difference between the 'chart audit process' and the 'audit of the chart audit process.'
Your clinical staff are auditing the charts. Ideally, they are looking for conformance to certain forms being included (and properly completed) such as consent, med reconciliation, treatment/care plans, etc. Even more, they are hopefully reporting more than just the % compliance but trends that can be actioned. If there is, for example, a particular team/unit with consistently lower conformance rates. This chart audit process should be aligned to clinical requirements - accreditation, college, pick your source.
From an ISO 9001 perspective, you're likely looking to confirm that they are are following their process. You are not necessarily looking to see if they included properly completed consent forms (although, this could come up during a sample record check), but rather that they follow their chart audit process.