Chrome has Flash Player built-in, that's not in any way a relevant way to verify an FP insdtall. The rest is too vague to make sense, since you didn't provide any system information or otehr technical details.
Moving this discussion to the Installing Flash Player forum.
As Mylenium said, Google Chrome comes with it's own embedded Flash Player. Updates for flash player come through Google Chrome's update and can't be installed manually.
If you are installing flash through Adobe's installer/updater, you are only effecting the use of Flash Player in Internet Explorer/Mozilla.
If you cannot see flash in Google Chrome, you may want to check and see if the plugin is enabled.