My boxwood flutes all prefer humidity. I keep them humidified in the winter, I can leave them out in the (DC) summer. What you don’t want to do is shock it – that is, give it extremes in humidity.
Yeah, what you want to avoid is not playing it for a week, then playing in a session for six hours, then taking it to Tucson. Assuming the wood was seasoned properly, the normal fluxes of the seasons shouldn’t give you too much trouble. You may experience your tenons swelling, so you’ll need to adjust the lapping accordingly (i.e. sanding corks or removing a layer of thread).
Should be fine, just don’t humidify it. (That’s right, I said do not.) Since you’re playing it every day, and you’ll be in Florida, don’t humidify the flute while you’re there, even if you live in air conditioned comfort. Why? It’s easy to over humidify Boxwood in Florida, which can lead to a bloom of the dreaded “Blue Streak” mold that lives in much boxwood.
I had a very nice Fred Rose Boxwood whistle when I lived in Florida, I kept it humidified, because I lived in a very air conditioned apartment (I kept it particularly cool in order to keep my dog comfortable, since German Shepherds are a double coated breed), however regular playing would have been enough to keep it properly humidified, so I ended up over humidifying and the fungal spores that cause blue streak bloomed like crazy.
Simply play your flute, swab it out, put it back in the case/roll or whatever, and you’re good to go.
By weird quirk I have not one, but two boxwood flutes. When I wrote Olwell’s shop about tenon maintenance on the one, Kara Lochridge wrote me back and said in their experience boxwood is happiest between 50 and 55% humidity.