Are you referring to the embedded version used by Edge/IE? Please post a screenshot of the Control Panel item you're referring to.
[Your] initial post is a bit confusing. Background Updates will not disrupt your work. When Background Updates determines an update is available, it downloads and installs Flash silently in the background. If the browser is in use, it'll continue to use the existing version of Flash Player until the browser is relaunched, at which point, the newly installed version will be loaded by the browser.
Not this one. This one demands control of my entire computer and does not run in the background. It's obviously not just for Edge, or it wouldn't order me to shut down Firefox in order to uninstall it, and it wouldn't insist I close Chrome in order to update (which is what I referred to in my initial post).
If you have Flash Player set to "Allow Adobe to install updates (recommended)", it will update silently and not interrupt your work.
If you choose Notify me to install updates, you'll get a notification prompt and you'll get the manual installer. I'm pretty sure that this is what you have selected.
It's also worth noting that there are three (major) variants of Flash Player on Windows, which correspond to the plug-in interfaces provided by the three major browser vendors. There's ActiveX for IE and Edge (which are managed via Windows Update on Windows 8 and higher), there's the NPAPI interface for Firefox, and there's the PPAPI interface for Chrome and other Chromium-based browsers (Opera, etc.).
My guess is that you're getting multiple notifications because you've installed both the PPAPI and NPAPI plug-ins, and they both need to get updated, but require separate installers. We also probably rate-limit those update notifications to once per day, so you're getting one for NPAPI and the other for PPAPI once the rate limit period expires.
The shim installers *do* delete themselves after installation, which is by design. There's another group inside Adobe that provides the installer technology, and I can't speak authoritatively to that rationale, but it's definitely intentional.
There's a reason that we recommend turning on automatic updates. It's a way better experience, and you get security patches quicker, since they don't require human intervention.
Hope that helps!
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