Where is the word "cutlery" in common usage
In the United States, cutlery is a formal (read: pretentious) word for cutting and peeling implements, that is, knives and paring utensils. I am primarily familiar with it from department store signs, and perhaps the decline of department store shopping contributes to its declining usage, like calling bed and bath goods domestics.
Cutlery in the British sense encompasses all eating and serving utensils, for which most Americans would say silverware or flatware, regardless of shape or material. This usage of silverware sets it apart from other types of -ware which refer to the material (e.g. glassware, plasticware) or the use of the item (e.g. housewares, giftware).
Martha Stewart calls it flatware, and that is good enough for me.
Macmillan flags cutlery as "mainly British," and goes on to note that the usual American word is silverware. (Which apparently has other connotations in British English.)
Another chiefly American synonym is flatware.