How can I create a psychedelic pattern with paint on a flat surface?

You can do a spiral effect from the center outwards by using spray paint, and by leaving a space as you spiral the paint you can add different colors into the same spiral. Or you can spatter paint the board using a stiff brush ,like a scrub brush or very stiff paint brush dipping it into paint and then using a rubber glove so not to get paint on your hands pull back the bristles and it shoots the paint on in no particular pa tern . And you can use different colors also on the same board. It look neat when you are finished if you do it right . Then just finish it up with a couple coats of Clear acrylic enamel, to protect the paint.

Spray paint is tough, if your gonna go that route do it close so its thick and stays wet, get all the colors on an scratch zig zags with the end of a paintbrush down every other spiral, id prime it and do a watercolor wash

You should use a coat or two of primer over the wallpaper. I suggest Kilz2 interior/exterior latex. One coat may do it since you already have it slightly covered. Then use regular interior latex paint in the color of choice for the top coat.