Hi Tsui, I have a Chromebook myself. The approach that usually works on non-Chromebook computers requires your Chromebook to be in developer mode. Putting your Chromebook in developer mode wipes your local data and makes it yell at you every time you boot it up, so I don't recommend it unless you really like tinkering.
Instead, you can tell Flash to delete local data from within the browser. This will delete any characters that have not been "saved as file", so start CoC, load up any characters you want to keep, and save them to files via the Data menu. Once you've done that, right-click on the game screen and choose "Global Settings..." from the context menu.
This will take you to a webpage titled "Flash Player Help". From the left sidebar, in the "Settings Manager" section, choose "Website Storage Settings panel". This will show you a page with an embedded widget. At the bottom of the widget is a box with a list of sites you've visited that have flash apps with stored data on your computer, one of which should be "local". If you're sure you have all your characters saved that you want, choose "local", then click the "Delete Website" button.
Refresh the page running CoC. All achievements should now be locked, and all characters wiped. Load up your characters from your save files and you should be good to go.