indiandave is right. You'll need to clean that revolver very well after using black powder.
And clean it with soapy water. Black powder contains salts that are only dissolved by water. Petroleum-based cleaners will not dissolve the salts and carry them off.
You will also need to clean those cases, after they've fired black powder.
The easiest way is to get a quart jar, fill it with water and a few drops of dishwashing liquid (the sink type, not the automatic dishwasher type). Screw the lid down tight.
After firing that ammo, use a long, skinny nail to knock out the used primer from the inside of the case.
Drill a 1/4 inch hole in a piece of scrap 2X4 for the old primer to drop into.
Now, drop the deprimed cases into the jarful of soapy water. Shake it for a few minuutes. Drain.
Now, with a small bottle brush or even a patch on a cleaning jag, scrub out the interior of the case while under the tap.
Place cleaned cases on a shallow baking sheet. Put them in the hot sun, or even in an oven at its lowest temperature with the oven door cracked open a bit.
This will dry the cases quickly.
The same soapy water solution can be used to clean the chambers and bore. The patch only needs to be moist, not sopping wet.
A brush run up and down the bore will loosen fouling after you've run a through damp patches through.
Use a small square of damp cloth to wipe black powder fouling off the frame, paying particular attention to the area where the barrel screws into the frame.
An old toothbrush gets into tight areas around the frame.
With a damp patch, clean the hammer nose and the firing pin areas. Dry with a clean patch if necessary.
Cap and ball shooters, like myself, often disassemble the entire revolver down to its screws and assorted parts, dump everything into a tub of soapy water, and scrub away. Then we rinse the parts and dry them in the oven, as above.
Once dry, the parts are oiled and reassembled.
It's the age-old way of thoroughly cleaning a cap and ball revolver and is still the best.
But you don't want to start disassembling your modern revolver!
Or, perhaps you could trade those black powder .38 Special cartridges to a Cowboy Action Shooter for smokeless powder cartridges and avoid the whole cleanup.
It's up to you.
Some of us like the sulfurous smell of blackpowder.
I love the smell of brimstone in the morning ... it smells like ... history.