So I have a cycle cross carbon fiber frame and an alloy seat post (Not a carbon fiber seat post) and was wondering if I'm likely to do any damage to the seat tube if I attach a Blackburn seat post rear rack along with a rear trunk bag that likely won't have more than 5 or 6 lbs in it. The rider is about 175 lbs. and will only be used for the occasional two day overnight adventure.
As always, thank you for your input.

Unlikely to damage the bike frame or post, but the Blackburn could use more bracing.
I bought a relatively cheap rack off Amazon and used the included seat stay mounts for added support.
You will notice threaded points mid-rack that allow using adjustable stilts that clamp low on the seat stays.
Also helps prevent your load from engaging with any part of the rear wheel.
The rather expensive Blackburn can otherwise fail at a key weld from the jolts and vibrations.
No need to ask me how I know...

Things like this are chances to carry more weight the 5 or 6 pounds and even though you might have a long tight fitting seat post that is constrained with reinforced carbon at the ST, TT and seat stay joints it would make me nervous.

I have both a Topeak and a Blackburn seatpost racks on road and gravel bikes. The Backburn lives on an older Spec Roubaix, which has a carbon seatpost, now for many years. The bike I use for 'social' rides, Have had up to low teens lbs. in the pack. Never a problem.
The other on a Poseidon X with alloy post, which goes on and comes off, depending on need...
Never a problem on either....
Thing I worried about the most when first setting up and using, was crushing or cracking the seatpost.. I found a 1mm thick tough but flexible piece of urethane I would tape under where the rack would clamp onto the post. Lets put it tight without crushing and also keeps the rack from swiveling side to side...
Never a problem on either setup...
No idea wher/what the urethane piece was for or came from, just something sitting around in my workshop...