A red flag next to a Requisition or a Task means that the Requisition/Task has passed it's due date. The system displays this red flag even if the Requisition/Task has been completed. For this reason, users will eventually see a red flag next to every Requisition on the Requisitions page in MyServices.
This is among a number of items related to changes in the business engine that have been requested by many customers, however, it is not on the road map for a near-term release. I encourage you (and all customers) to submit enhancement requests for these types of features, since that carries a good deal of weight when features are prioritized.