I've been having this annoying little issue lately. I am unable to install or update flash in all browsers on my Macbook Pro. I've listed the issue and steps below. I've already wasted 3 hours of my morning searching Google for an answer instead of coding.
Note: I was able to download the file via a PC in Firefox, upload it to Dropbox and install on my Macbook Pro. However, I was still unable to download or update Flash even after installing the latest version. I also tried uninstalling and reinstalling Firefox with no luck.