Is lymph flow propelled by the contractions of the heart?
No, the lymphatic system is not connected to the heart.
The heart is a big pump responsible for moving blood through veins. However, the lymphatic system is separate from the blood circulation and doesn't have such a pump.
Lymph is brought into motion by contraction of smooth muscle cells in the wall of the lymph vessels (see image). These muscle cells contract rhythmically and form the intrinsic lymph 'pump'. Lymph flow is further aided by the normal movement of the body i.e. action of skeletal muscles.
To ensure that lymph flows in only one direction, the lymph vessels contain valves . These valves are also present in veins and the heart to prevent backflow (see image below).