How is food transferred in flatworms without a circulatory system?

By diffusion

Explanation:

Flatworms are acoelomates, that is, they do not have coeloms or body cavities. This results in a flattened body that is devoid of circulatory or respiratory organs.

The flattened body enables easy diffusion of much needed nutrients and oxygen from their surroundings into their bodies. Excretory products within the body are removed by diffusing the other way round.