What bookmarks are you talking about ?
I use avast free 17.5.xxxx and Firefox as my primary browser on all three systems and I have never lost bookmarks if a reinstall or clean install has been done.
I can only assume that you are talking about the SafeZone Browser ?
If so it is possible, open the AvastUI > Settings > Components - now click on the ? top right of the screen (context menu help) > Security components overview - scroll down to the SafeZone Browser and click the Read more... link. Now you have a list of options - including - How do I import bookmarks from the previous SafeZone or from other browsers? - open that.