I did a quick search through my stuff for period mentions of cleaning guns by washing them with water and found a few which might be interesting to some.
Spence1764
Bouquet's March to the Ohio, the Forges Road (From the Original Manuscript in the William L. Clements Library), edited by Edward G. Williams: The Historical Society of Western Pennsylvania. p. 103-4.
“After the Arms have been drawn & fired off they must be washed clean and remain unloaded till further Orders."
About 1785
David Thompson’s Narrative of his Explorations in Western America 1784-1812
“The same evening Wm. Budge, a fine handsome man, John Wellam, and the Indian woman were frying pork and grouse for supper, [when] the smell attracted a Polar Bear, who marched to the Tent, and around it, his heavy tread was heard, and no more cooking thought of. As usual in the evening, the fowling pieces were being washed and cleaned, and were then not fit for use, but there was a loaded musquet.”
1789
An Essay on Shooting, Wm. Cleator
114 “There is a curious circumstance attending the shot of barrels, which is, that sometimes the grains of lead, in place of being equally distributed over the space they strike, are thrown in clusters of ten, twelve, fifteen or more, whilst several considerable spaces have not a single grain in them”¦. Mons de Marolles says, that this is especially the case when the barrels are new and also when they are fresh washed.”
207 “ A fowling-piece should not be fired more than twenty, or five and twenty times, without being washed;”
1846
Instructions to Young Sportsmen in All that Relates to Guns and Shooting, P. Hawker
pg. 47 “Let your barrels be first washed perfectly clean with cold, and then fill each of them with hot water; which by the time it has nearly run out at the touchhole, will accelerate their being wiped dry, as much as though boiling water had been used; and before they have completely discharged the water; stop the muzzles and touchholes; and after shaking it up and down in the barrels, turn it out at the muzzles, by which means you will effectually stir up and expel any extraneous matter that may have lodged in the bottom of the chambers.
“I have recommended washing guns with cold water, from having found that it always more readily removes the foulness occasioned by the powder, which, from sudden heat, is apt, at first, to dray and adhere more closely to the caliber: whereas with cold water, it remains in a moist state, and immediately mixes."