Spring is the best time. Collecting birch sap too...yum!...(btw, unless you are far north, its probably too late for sap collecting this year.)
Try cutting about 1/2 way thru and peel off around tree circumference. Going too deep girldles the tree what will kill it. The bark will grow back. When I lived in europe we had trees what harvested multiple times over the years.
Flatten it between boards or something whilst it dries. Its several weeks to get really dried. Otherwise it curls up tight and much harder to use. My grandmother from Finland made various things of it. Weaving strips to make baskets, lampshades even knife scabbards. When I make knifehandles, usually glue many sheets in my press to make slabs about 1” thick. Those are cut to blocks for stacking on sticktangs. I like making slabs, under my 20 ton press, ends up better density and uniform thickness rather than stacking individual layers on a tang. Also, with uniform thickness, if I put accent spacer between layers their spacing better uniform. Also, grain direction factors also. If grains all one direction, after sanding & polishing creates an irradecence sheen what changes as handles is rotated in the light. Alternating grain while better durability, defeats that optical effect.
Good luck. Sadly where I live now birches are wrong species their bark is not good for much. My buddy from northern BC Canada keeps me supplied.
