Snug a scrap piece of flooring against the casing, as shown, and place a flush-cut saw blade flat against the scrap. Score the casing on low. Make more light passes, ramping up the speed each time, until you cut through the trim.
Tip: "You can't push the saw blades for these tools too hard or you'll end up with sloppy cuts and worn teeth. It's better to take your time and make shallow passes."
—Tom Silva, This Old House general contractor