Cricut Design Space is full of problems. Provo Craft are little or no help. I don't think you will get much from Adobe as they haven't written the plugin.
The Explore is a great piece of hardware but it is really let down by the only software to work with it, when it works.
You best port of call is YouTube. There is a lot of advice there. Make sure it is a recent video as Provo Craft changed their plugin in the last couple of months?
As you have noticed Design space is extremely cranky to say the least. DS customer service blames or on everything from user error to slow systems. I am surprised they haven't told you to go out and buy a new system. This however doesn't answer your question. I am truly not sure their is an answer. One thing I would try is to disable your antivirus when downloading. I know some of us have received an error. This might help. Wish I could be more of a help. I pretty much have a pretty paperweight. It seems. I can only use DS on off hours it seems that they just don't have the server capacity. So I get my least problems in DS at 0100-0300 in the am.
I'm not familiar with the product you are referring to. Is the installer coming from the Design Space software, or the Adobe website?
What OS, and version, are you using? I'm assuming OSX, but not sure
Google integrates Flash Player in Chrome, so there is no separate Flash Player to install for Chrome.
Flash Player is a browser plugin, not an application, therefore, it won't save anything to the Applications directory.
Please post a screenshot (see The specified item was not found.) of the error message you are getting.