In Outlook Web App (OWA) I'm seeing two different functionalities that sound like what you are describing. There is the red flag that can be set to different times that the task/email should be completed by and a color (rectangle) category that can be set
on the email.
If you log into your OWA and click the highlighted rectangle that is show in the example above, you should see a list similar to the image below appear.
Which will then allow you to assign a category to the email in question.
If the information above doesn't help, please reach out to one or both of the communities linked below for assistance from the IT Pro audience in the TechNet community: