grainy vintage coloring

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1) Duplicate your image then go to Filter> Noise> Add Noise. Set the amount to 12.5% and the Distribution as 'Gaussian'. Make sure the Monochromatic box is checked.

2) Set the layer mode to 'Luminosity' and the opacity to 14%. Then duplicate that layer and change the layer mode to 'Soft Light' and the opacity to 32%.

3) Coloring

Brightness/Contrast
brightness: 59
contrast: 0

Gradient map

point 1- #fb6070 location at 0%
point 2- #ffcc00 location 33%
point 3- #c8ff2b location 69%
point 4- #00e7bf location 100%
Set the gradient map layer mode to 'Multiply' and the opacity at 42%

Color Fill

#081536
Set the layer mode to 'Exclusion' and the opacity stays the same at 100%