Draw the line art on its own layer
Duplicate the line layer if needed
Select the line layer
Tap Adjustments
Tap Gradient Map
Choose a rainbow gradient or create one
Adjust the gradient stops to fit the colors you want
Use Alpha Lock on the line layer if you want the effect only on the lines
Or use Clipping Mask with a color layer above the lines
Set the color layer blend mode to Color, Overlay, or Soft Light
Paint or fill the clipped layer with rainbow colors
Use Gaussian Blur slightly if you want a softer rainbow glow
Duplicate the rainbow layer for stronger color
Lower opacity if the effect is too intense
Merge layers only after you are satisfied