When I'm logged in I can view my flagging history but only for those flags that I have raised on posts and comments.
What about the flags that I have raised for chat messages? Is it possible for me to track the status of those flags?
There is no option to track chat flags.
In fact there won't be any url to the flagged messages to track.
Chat flags will be approved or declined very soon since they can be reviewed by users with 10k network wide reputation and all the moderators.
Once you have flagged a message as spam/rude, a red flag marker will be shown beside that message. If your flag is approved, the number increases. Eventually the message disappears.
If it is declined, the message stays. That is how we know if flag is approved or not within minutes.
Since chat is less formal, rude messages are deleted quickly. It is suggested to check the room environment before flagging as rude.
Source : I have network wide reputation greater than 10k to review chat flags and personal experience.