I'd rather use the newest version, and (starting from Chromium 35, I believe) you can only use Pepper Flash. BUT I'd rather avoid closed source software as that implies a security risk if the code isn't under public scrutiny.
Am I correct?
Being open source does not necessarily mean the code is going to be scrutinized by the public, or that it will be fully audited and properly scrutinized, even if it is. It simply means that it can be.
For Flash, you don't have much choice. There are some open source Flash plug-ins, but a very large number of sites just won't work in them, as the sites will require much newer versions of Flash. Whether you are using the Pepper based plug-in that Google builds in Chrome (Chromium is open source and will not include the Flash plug-in), or the last supported version of the Adobe Flash plug-in that is available, you are still using proprietary software. The only true way to not use proprietary software is to not use Flash at all.
No, Pepper Flash isn't unsafe because it isn't open source. Google is investing a lot of resources to work on Pepper Flash and keep it safe and secure. The software model is a very secure one and you shouldn't worry about using it.
If you want to stay as open source as possible and still retain a lot of functionality, Chromium is the way to go.