I have an early 19th century boxwood flute and also a boxwood piccolo and did some research on them. I'll share relevant parts of what I found re the wood and staining.
"A relatively lightweight, fine-grained, slightly porous, unstable, polishable, dense hardwood.... Boxwood gradually changes in color from light yellow to a yellow-brown over a period of time. Boxwood flutes that are dark brown in color have probably been stained by use of a chemical such as nitric acid. Boxwood is not good at retaining its shape, since it is porous, absorbs moisture readily, and often contains unstable "reaction wood", probably from not growing vertically. Due to these problems, it has a tendency to warp, crack, and bend with changes in humidity.... Despite these drawbacks, boxwood was a popular material for making the tubes of transverse flutes and recorders in the Baroque and Classical periods. This is probably due to its availability, beauty, easy workability, and the reputed 'sweet' sound produced from flutes made of this wood.... Careful selection and preparation of the wood, thorough seasoning and stress relieving by the flute maker before starting to make the flute, and careful adherence to the maker's care instructions by the new owner makes the warping and cracking of boxwood less likely."
