Duplicate FPS from 24" barrel with a 16" Barrel

Rule of thumb? No

The charges/amounts/types in the manuals are based of chamber pressures and the velocity is the tail end of that process.

Your velocity will be lower with a shorter barrel, to increase speed you would need to increase the amount of powder. HOWEVER, if you want to be subsonic you would want lower velocity.
 
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If you're loading it yourself, which it sounds like you are, just load up 5 rounds at a time with 0.1 or 0.2gr increases and see what the differences are. That will tell you what you're looking for.
 
Looking at Hodgon subsonic 223 and 308 with Tite Group load data today and their data is based off a 24" barrel. Is there a general rule of thumb for powder amount to use with 18" and 16" barrels to get the same basic FPS as the 24" barrel?
There probably wont be a big velocity difference, since you'll get 100% powder in both barrel lengths with Tite Group. You actually might get faster velocities with 16" & 18" barrels in this case. I'd start with a mid range load and work down (or up) if necessary. Gordon's Reloading Tool is very useful for modeling these type of situations - you can download it for free here:
 
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There probably wont be a big velocity difference, since you'll get 100% powder in both barrel lengths with Tite Group. You actually might get faster velocities with 16" & 18" barrels in this case. I'd start with a mid range load and work down (or up) if necessary. Gordon's Reloading Tool is very useful for modeling these type of situations - you can download it for free here:
This^^

People forget that you stop getting more velocity as the barrel gets longer then velocity starts to go down.
With Subs you may very likely see higher FPS with an 18" instead of 24"