The only pockets I’ve ever seen on a Regency gown are watch pockets. They’re small, right at the “waist” (i.e. under the bust where the skirt meets the bodice), and set off to one side. In the picture here you can just see the watch pocket gaping open slightly under the right sleeve.
The watch would have been worn round the neck on a long chain, or the chain could have been attached to a broach.
I've seen similar watch pockets on extant habits, but I haven't seen a side pocket in the skirt on any extant garment, not even on the redingotes or pelisses from the era. The earliest side pockets I’ve seen are on gowns from the 1830s, though they remain an oddity up until the 1860s, rather than a commonly adopted feature.It makes a certain amount of sense if you think about it, though. It's hard to have a pocket in a gown made of a light-weight fabric that's meant to show off the lines of the body, but it's easy won't the skirts get full towards the end of the 1820s, and there's plenty of petticoats to hide the bulge of whatever you might put in that pocket.
So my Georgian ladies can have pockets under their hoops, and Victoria Dahl's Victorian ladies can have pockets in their gowns, but should either of us slide into a Regency setting, we'll have to find a handy use for a ridicule (braining an uppity hero greatly appeals to me).