Meaning: This sentence is a simile that means the artist's emotions are being expressed in the painting in a smooth and easy way.
Choice of Words: Emotions are the feelings we have inside. Flow means to move smoothly and easily. Rivers are bodies of water that flow. Canvas is the cloth that artists paint on. When we put it all together, it means that the artist's emotions are being expressed in the painting in a smooth and easy way, just like a river flows.