If I flag behaviour by a moderator, is the same moderator allowed to decline the flag, or do they have to have it assessed by another moderator?
Related question: Restraining from moderator actions in issues you're involved in
If I flag behaviour by a moderator, is the same moderator allowed to decline the flag, or do they have to have it assessed by another moderator?
Related question: Restraining from moderator actions in issues you're involved in
According to Stack Exchange Team (email communication), moderators are not allowed to interfere with issues they are involved in. I believe this includes declining "flags about their own behaviour" as you mention in your question:
However, I do think there is a problem with a moderator using their privileged position to influence a conflict they are actively involved in. So it's not a good idea for a moderator to delete an upvoted answer to their own question. This is something we emphasis with new employees who have recently been given moderator privileges.
Later in the mail:
I am going to remind masked_moderator_name of the importance of that principle. If an answer really needs deleting, a moderator uninvolved in the controversy should do it.
While my issue was with a moderator deleting my answer on his question, I think the same logic applies when moderators interfere with a conflict they are actively in (e.g. declining flags on their own behavior).
If you are still unsure after my answer, it might be a good idea to contact Stack Exchange Team and ask them your question.
Technically, mods are "allowed" to dismiss any flag, in the sense that the system allows them to.
Practically, it depends on the flag and it might not be the right thing to do at all.
If the flag is generic and not really pertinent or clear, we generally dismiss them. This is not to hide anything, or avoid a second look. It's because more input is needed from the flagger to clarify the flag. If you want to have more eyes looking at something, your flag should be clear on what the problem is. For example if something is marked as "rude" and there's nothing obviously rude, then you might want to open a more specific flag clarifying what you mean.
On the other hand if the flag is specific (e.g. a "flag for mod attention" with a specific reason), then it should not be dismissed by an involved moderator (beside obvious bad cases like trolling, insults, spam, etc. but that's not what we are talking about here).
In any case, an active flag makes also all the older flags appear to mods. The timeline of the question also includes all flags.
Finally, keep in mind that diamond mods do involve each other constantly on Skeptics and keep an eye on each other independently on flags: the number of posts on the site is low enough that each post gets commonly 2 or 3 mods looking at it.
To recap:
if you want a second pair of eyes on something, flag for mod attention and say so, with specifics to help the next mod.
as usual, if you want a third pair of eyes, do involve the community team.