I don't use any 'windows', but in Linux (KDE or Enlightenment desktops) look in the following location. the 'xxxx' will be a bunch of characters. Stylish is stored in an .sqlite 'database'. I'm using DB Browser for SQLite right now. It seems pretty good under Qt, but miss SQLiteManager.
~/.config/google-chrome-beta/Default/databases/chrome-extension_XXXXXXXX in my case, the db is named merely '2' as it must have been the second extension needing a sqlite db I installed.
I copied '2.sqlite' to anther instance of Google-Chrome (Chromium actually). You NEED to install Stylish for Chrome FIRST. Backup ('compress here', rename or tar) the installed, default db Copy the db ('2') to the Stylish extension directory, renaming it to the bd created when the stylish ext was added.
Start Chrome / Chromium and click on 'Stylish button' and choose 'manage installed styles'. You should see all your styles you built on your 'other' instance of chrome.
Hope this helps someone. Landis.
ps, i don't have an easy way of telling which extension directory is for Stylish. You need to open each db and see if the 'style' Table exists. If it does, look in Table section_meta. You should see the effected urls for the styles you've created.