Use GoodLinks browser extension to save links to GoodLinks app.
After installed, click the GoodLinks button to sign in with your Apple ID. The extension runs completely client side, communicates only with Apple's iCloud to save your links. It does not collect or pass anything through any other servers.
Default keyboard shortcut for the extension are Command+Shift+S (Mac), Ctrl+Shift+S (Windows). You can change it in the Chrome Settings for Extensions.