The widespread adoption of Internet of Things (IoTs) and edge computing devices has made them an integral part of our daily lives. The popularity of these devices has surged, especially with the advancements in wearable technology, such as smartwatches, health and fitness trackers, and smart glasses. These devices are equipped with various sensors that allow researchers and manufacturers to capture user data, which is then processed using on-device Machine Learning (ML) algorithms to enhance the user experience. However, running ML algorithms on these small IoTs and edge devices consumes a significant amount of power and energy. It is crucial to note that these devices are designed with tight energy and power constraints. Optimizing battery usage is paramount to prolonging the longevity of these devices. This paper proposes a framework that efficiently harnesses kinetic energy harvesting to intermittently support ML computations/tasks, thereby reducing the load on in-built battery. The primary goal of the proposed framework is to reduce the reliance on the device's built-in battery power by offloading the ML computation to harvested kinetic energy. This framework integrates energy and memory-efficient checkpointing with Energy-aware Early Exit Neural Networks to manage harvested kinetic energy optimally. Through experiments and analysis, the results demonstrate that the proposed framework effectively utilizes harvested kinetic energy to perform necessary ML computations during inference/testing, thus reducing the energy footprint.