Finlets have a unique overhanging structure at the back, similar to a flag. They are located between the dorsal/anal fin and the caudal fin on the sides of the body. Until now, the sensing ability of finlets has not been well understood. In this paper, we design and manufacture a biomimetic soft robotic finlet (48.5 mm long, 30 mm high) with mechanosensation based on printed stretchable liquid metal sensors. The robotic finlet's posterior fin ray can achieve side-to-side movement orthogonal to the anterior fin ray. A flow sensor encapsulating a liquid metal sensor network enables the biomimetic finlets to sense the direction and flow intensity. The stretchable liquid metal sensors mounted on micro-actuators are utilized to perceive the swing motion of the fin ray. We found that the finlet prototype can sense the flapping amplitudes and frequency of the fin ray. The membrane between the two orthogonal fin rays can amplify the sensor output. Our results indicate that the overhanging structure endows the biomimetic finlet with the ability to sense external stimuli from stream-wise, lateral and vertical directions. We further demonstrate, through digital particle image velocimetry experiments, that the finlet can detect a Kármán vortex street. This study lays the foundations for exploring the environmental perception of biological fish fins and provides a new approach for the perception of complex flow environments by future underwater robots.