You can have dock badges show up by using a userscript from userscripts.org
Step 1: Open Preferences (cmd+,)
Step 2: Click Show All, And then click General
-Make sure "Fluid attempts to show Dock badge labels" is checked
Step 3: From the Script Menu at the top (the script icon) choose browse Userscripts.org
Step 4: on Userscripts.org search "facebook fluid"
Step 5: click the script you want, I chose "Facebook Dock Badges - Inbox & Notifications" on the subsequent page click the big "Install" button.
Accept all the following stuff, and restart your Fluid app.
I can confirm that this works for me. (Make sure you have the latest Fluid)