New document

Open a new document, my dimensions were 380x300

Clouds Effects

Filter > Render > Clouds

Short Strokes

Filter > Pixelate > Mezzotint > Short Strokes>

Radial Blur

Filter > Blur > Radial Blur (Check Zoom, Amount 100, Quality best)

Preview

Press Ctrl + F, so far your design should look like this

Duplicate Layer

Layer > Duplicate Layer

Twirl Effects

On the duplicated layer, Filter > Distort > Twirl (Amount 100)

Blending Options

Right Click on the layer to BLENDING OPTIONS, blend mode: lighten

Merge

Ctrl + E for to merge the 2 layers, it should look like this now:

Choose Colors

Image > Adjustments > Hue/Saturation, check on COLORIZE and choose your colors.

Layers

Duplicate the layer and set the blend move to OVERLAY and fix up the opacity of the layer

Result

You are done! This is what your pic should look like: