Depending on how many colors you want to use, pour a few drops of different color oil paint into a baby pool halfway full of water and stir the colors together. You will notice that the paint remains on the surface of the water. You can add more colors or more of the same color paint until you get the desired effect.
After this, carefully slide a white poster board in the pool under the paint, making sure the shiny side faces up and allow the poster board to float to the surface and make contact with the paint.
Then carefully pull the poster out along the edge of the pool and gently lay it on the ground to dry.
This is a messy thing to do if you’re not careful. You can use tempera paints, but not water colors.
Another thing you can try is laying a white poster board on the ground, shiny side up. Then take a garden hose to it until it is fully wet on top, then take tempera paint and allow it to pour out of a small container from about 5 feet above the poster and let the paint splatter. Quickly do the same with your choice of other colors and let the splatters overlap until you have the entire poster covered. Allow time to dry.
I have filled balloons with water mixed with paint and taken a 4 X 8 plywood, painted white. I climb up the tree and drop several balloons and let them splat. People like this stuff. I don’t recommend this if you don’t first lay lots of drop cloth under it.
As far as using swirly paint in a baby pool, you might want to try dipping styrofoam balls using temera, not oil based paints and make your own solar system just for the fun of it. Using a basic wooden sticks like skewers to dip the balls of various sizes in the temera painted water swirls would be very effective.