We have done this one a few times.
I mix paint with some water to make it thinner, this way it is easier for the syringe. I lay lots of cotton wool down and then leave Button to it.
This helps her build the strength in her hands and fingers and hand eye co-ordination. She even did some colour mixing with this. sucking up two different colours to make a new colour.
She enjoys this everytime we do it and has actually asked for this activity on a few occasions.