Probably at least daily taking it down and oiling all metal, cleaning the wood, keeping a tompion in the barrel to keep insects/etc. out of the bore. Very prompt and religious cleaning after an use. Humid air conditions played havoc. Probably the actual care routine wasnt too much different than ours now, but certainly in practice care was much more frequent and detailed. I have read that in the 1800s, metal was sometimes varnished , frequently heavily waxed to protect it. Even in the early 20th century here in northern NY (a notoriously wet environment) it wasnt unusual to varnish blued arms. Looked like hell. I have seen a number of arms so treated. I have heard the powder was stored for longer periods in lead cylinders with a fitting lead top, sealed with wax.
I love reading of early explorers/hunters, and unfortunately few of them detailed the simple to them daily care routines of thier trips like you inquire about.
Nowadays with my flintlock in typical wet fall conditions....if it is raining...we stay in. You didnt hunt in the rain, and battles were frequently postponed if raining (even native americans chose not to fight in the rain...bow strings went to hell when wet). If a light drizzle, maybe hunt, if I am going to be sheltered. At the end of a wet day, the arm is discharged/load pulled, and a thorough drying and cleaning, leaving the arm near the fireplace to thoroughly warm and dry out before assembly if possible. It will not be loaded until immediatly before the next hunt. with reasonable care, no rust after decades of use.