I tried to find this in Chromium's website but the don't mention it. I know that that Chromium 32bit comes with the Flash plugin included, but does the 64bit version include it too?
No. Chromium doesn't include Flash, at least the upstream version doesn't. Chrome, the closed source version, does include flash, and this is the source for the confusion. You can check the main differences between Chrome and Chromium in this page.
Chromium supports NPAPI plugins, and it will use the system wide flash install if it's present, like Firefox does. So flash will work in Chromium if you have it already installed.
This applies to both 32 and 64 bit versions.