I have "notify me before breaking everything" selected, but this does not stop Adobe from breaking everything, and since Flash is updated weekly or so, this is extremely irritating. Almost as irritating as the barriers intended to prevent anyone in authority at Adobe from hearing about these problems. WTF is wrong with you people?
What version of Flash Player are you trying to install? As of Flash Player 126.96.36.199 (latest version), Flash Player no longer requires the browser to be closed for installation, unless re-installing the same version as files in use can't be deleted/replaced.