[Greg Jones]

No, flagged items have the same color as the status-based styles that are displayed, depending on the item's status. One of the challenges of adding a custom color for flagged items is that you will have color conflicts. If a flagged item could be set to display in say green, what color would it have if the task was also overdue?

You can already see this conflict in the default status-based styles as a blocked item is, by default gray while due soon/overdue items are orange and red, respectively. If a blocked item becomes due soon or overdue, it inherits the color for that status and no longer has the gray text to indicate that it is also blocked.