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
From Chrome users, you can select the user profile to be searched in the Web Bookmarks preferences.
As the demand for Firefox bookmarks support has been very low, we recommend synchronising your bookmarks to Safari, and using the built-in Bookmarks feature.
Users can sync their browser bookmarks to one of the supported browsers, or using an Alfred workflow to search Firefox Bookmarks. You'll find some of these workflows on Alfred Forum.