How can I achieve this vintage color tone in Photoshop?
A Curves adjustment layer gives you ultimate flexibility.
Edit each channel individually:
Red: raise the bottom left point.
Green: make a new point in the center and drop it slightly.
Blue: raise the bottom left point and lower the top right point, then make a new point at the center and drop it slightly.
Experiment with the opacity of the adjustment layer to vary the intensity of the effect.
You might as well want to look for an effect called "cross processing". Although I am aware it is not totally the effect of your example picture, but the principle is the same.