Very well at least, and even excellently on harder strop materials like wood, for most popular cutlery steels; anything from 1095 up through VG-10 & D2, for example. The most wear-resistant steels, like S30V and others with heavy vanadium carbide content, will always do better with diamond/CBN compounds. But most anything else I've tried seems to respond pretty well to Flitz, especially when it's used on wood. The one possible downside with it is, it seems to need refreshing/recharging on the strop pretty often; it works well, but slows down with more use and heavy strop loading (of swarf). This is also somewhat true with other 'polishing paste' compounds like Simichrome (seems to last a bit longer) or Mother's Mag paste. I've found it most handy as a quick 'spur-of-the-moment' strop, when applied as needed to most any piece of smooth, flat wood you happen to have lying around. I've used it on some wooden 'craft sticks' (also known as tongue depressors) for make-as-needed strops on the fly.
For longer-lasting compound that keeps cutting & polishing even with heavy loading of swarf, the 'sticks' of buffing compound used for buffing wheels seems to last longer. Two good examples I've used are Ryobi's White Rouge, and Sears' #2 'Cleaning' compound intended for hard metals like stainless steels. These are my two favorite compounds when used on hard wood-backed denim. The strops get quickly loaded with swarf and look filthy, but they keep on cutting & polishing, and will erase stubborn burrs very easily.
David