From Alfred 3.5 onwards, the Bookmarks feature was updated to include Safari and Chrome by default.
Take a look at Alfred's preferences under Features > Web Bookmarks to set up your preferred way of browsing these bookmarks.
Chrome bookmarks support
For Chrome users, you can select the user profile to be searched in the Web Bookmarks preferences.
Firefox users can synchronise their bookmarks to Safari to use the built-in Bookmarks feature.
Alternatively, it's possible to use an Alfred workflow to search Firefox Bookmarks. You'll find some of these workflows on Alfred Forum.