he Chromium developers have been working on extensions sync for some time, but this feature only became functional today. However, it is not available by default for now so you must manually enable it.
In case you don't know: Chromium is the open-source project behind Google Chrome so do not mix them.
If you wish, you can install Chromium 64bit instead of Google Chrome:
* The amd64 package is no longer using ia32-libs. It contains *native* 64bit debs.
Though you can now enable Flash on Google Chrome for Mac, the Linux still doesn't have support. However, if you're willing to run Chromium instead of the official Google build, you're in luck.