When a customer updates a case, the case owner usually receives an email notification. Often times that email might contain something like "Thank You" or "I need more time to respond" which doesn't require the case owner to respond, and therefore the flag should be cleared. These instructions will help you implement a shortcut link that opens the case and clears the flag in one click.
You can save case owners a click by adding a formula field to the case object that builds a URL that can be used in an email template to clear the flag.
1. Setup > Customize > Cases > Fields
2. New > Formula Field > (Provide a Name) > Text
3. Copy and paste the formula below into the formula field:
"https://login.salesforce.com/apex/FLAGS__FlagClear?id=" + Id
If you are using the My Domain feature in Salesforce, substitute "login" for "mydomain.my" where mydomain is the domain you selected.
4. Save the field and add it to the email template case owners are sent when their cases are updated.
Note that when the link is clicked the user will land on the case detail page, but the flag will have already been cleared.