These flags are needed but often do create a bit of noise. The best thing you can do is investigate whatever triggered them and flag accordingly to validate or invalidate them, which helps us clear them out of the queue more rapidly.
Let's look at what each flag is trying to tell us:
Possible vandalism of own posts
This flag is raised when a user makes a large amount of edits to their own posts in a short amount of time. 9/10 times, this is just an indicator that the user is maintaining and improving their contributions. On rare occasions, the flag will alert you to a rage quit, or a user trying to destroy their contributions before leaving.
Check the user's activity and look at a few of their recent edits. If there's nothing alarming, then flag as invalid. Otherwise, flag the same post that Community did as 'other' and leave a note that there's a rage quit in progress.
Please keep in mind that people often do go through their answers and remove posts that were down voted, or never up-voted. Additionally, people sometimes go through old 'tumbleweedish' questions and remove them. This is perfectly regular and normal behavior.
This flag is raised when the system finds that a user has posted the same question or answer multiple times. This one is almost always valid, and should be investigated.
Sometimes it's benign behavior, or a user just re-cycling an answer that is appropriate for several questions that are basically asking the same thing differently. Users should be providing appropriate context when re-cycling an answer, but that's not always possible, especially when the answer is just a few lines long. In that case, just flag as invalid.
If you see the same answer being re-posted on questions where there really needs to be something different about the answer for it to be useful, e.g. a sentence or two explaining how it pertains to the question, then you can either do nothing (leave the flag valid) or flag as 'other' and tell us what you think.
As Cody notes in comments, check for duplicate questions if the same answer adequately fits several questions.
Often, what you'll catch is people going back on old / famous questions and planting links to help promote their web site or product. If you see that, flag the same post that Community did as 'other' and let us know that we've got excessive self promotion going on.
As always, don't invalidate if you aren't sure. If you see something fishy going on, add your flag as a note to us, which also adds your weight to the flag causing it to rise closer to the top.
The flags that you mentioned are particularly noisy, so we really do appreciate the help of high reputation users getting the valid stuff to the top.