I'm pretty sure any use in the war was extremely limited if at all.
Tennessee had a lot of flintlocks left in their stores when the war began, supposedly leftovers from the Battle of New Orleans, and its possible there could've been half a dozen in there I would think. Beyond that I bet there were none from my limited knowledge.
The problem with them being run through the blockade is I highly doubt any were left to be sold off even as scrap in Britain by the 1860's. When the British decided to adopt a replacement in, I think it was 1835 or 36, what Bakers they had left were described as being completely wore out by some officers, so much so with advancing rifle tech a new rifle was desperately needed.
Combine that with Bakers supposedly being sold off to Mexico and other poor countries over the years, and I doubt any were left.
(Just got to mention, after reading archeology reports, I'm kind of halfway doubtful they were as common in the Mexican Army as a lot of books say. Maybe in the 1848 Mexican War, but Texas Revolution I bet they were next to non-existent. Sh** ton of evidence of Brown Besses, even in the light companies where Bakers should've been, but very little to any of Bakers I've seen.)
Now for the Baker's replacement, the Brunswick, there were a few. It had been replaced in 1853-ish, and the second model which bears an outward resemblance to the Baker only percussion, those made it over in a modified form with P1853 style rear sights.
Brunswick Rifle Confederate Purcahsed
collegehillarsenal.com
@Grayrock Volunteer can enlighten anyone on that rifle if he wishes.
On a side note, as a fan of the hokey
Sharpe tv series, I love the Baker.