Would this happen to involve a GoDaddy email account? If so, please have a look at this question to see if it a preferred sender issue and report back.

Tonnes said

Would this happen to involve a GoDaddy email account? If so, please have a look at this question to see if it a preferred sender issue and report back.

No GoDaddy email account was involved. Just Microsoft Outlook :)

I’m not sure whether you mean an Outlook.com account or the Microsoft Outlook stand-alone client, but think the same applies - apparently "flagged" in Outlook means "starred" in Thunderbird, like with GoDaddy. Either way, assuming you have set an outlook.com email account/address set up as IMAP in Thunderbird, the first thing you should do is view the Outlook webmail content - you should see all messages flagged there too. When viewing your Inbox in Thunderbird, a star should vanish as soon as you remove a flag in webmail, and vice versa.

Thunderbird has a filter option for starring messages using Message Filters, but I assume you did not set it up (or you would know), so the question is what flagged your messages in Outlook. I would say you have some filters set up to automatically mark (flag) specific messages or senders, but according to this thread on technet.microsoft.com, automatic flagging should only be available in the Microsoft Outlook client, not on outlook.com. That makes me wonder: could it be you are still (or also) using Microsoft Outlook as a client applying such action?

Does this help a bit and if not, can you be more specific about your account/email address (or rather: domain, not full address)?