I too have a Flobert rifle like yours. DO NOT use U.S. made CB or BB caps in this rifle. This may be my first post on this forum, but I can tell you that at the very least you accuracy suck when you are dodging the self ejecting brass.. My opinion and worth what you pay for it.
Before firing the Flobert I did a lot of homework. It is in fact chambered for .22 short and is resonably accurate at 25 to 50 yards. The best iI could date it was 1895. I was purchased originally by my great grandfather. I am looking for a replacement stock but no luck. I dont shoot it much but I keep it clean. The Winchester 1902 Was purchased by one of my grandma brothers around 1915. I did a restoration on it and got the black spray paint off it.