The ornamental design for a fingerprotector and nail covering kit, as shown and described.
FIG. 1 is a side elevation view of a finger protector and nail covering kit showing my new design;
FIG. 2 is a rear elevation view of the finger protector and nail covering kit;
FIG. 3 is a front elevation view of the finger protector and nail covering kit;
FIG. 4 is a top plan view of the finger protector and nail covering kit;
FIG. 5 is a bottom plan view of the finger protector and nail covering kit;
FIG. 6 is a top perspective view of the finger protector and nail covering kit; and,
FIG. 7 is a top perspective view of the finger protector and nail covering kit. The human hand and nail polish applicator shown in phantom lines illustrate how the claimed design is used and form no part thereof.