FIG. 1 is a perspective view as viewed from a front direction thereof of a rechargeable flashlight/nightlight showing our new design; FIG. 2 is a top plan view thereof; FIG. 3 is a first end view thereof; FIG. 4 is a right side view thereof; FIG. 5 is a left side view thereof; FIG. 6 is a second end view thereof; and, FIG. 7 is a bottom plan view thereof. The broken lines shown on the drawings are for illustrative purposes only and form no part of the claimed design.