The first thing to do with your particle system is to set the Initial Color or Color / Life module to Distribution Vector Particle Parameter. This allows the blueprint to communicate with the color. You must name the color parameter in the Parameter Name box. If you do not want your colors clamped to the 0-1 space, you need to set the Param Modes boxes from "DPM Normal" to "DPM Direct." If you want the color to be clamped, then leave the boxes as DPM_Normal.

If you would like to control the alpha as well in your blueprint, do the same thing there.

Ignore the comment box saying "Set Beam Color"

In your blueprint, after dragging the particle system into it as a component, use the node Set Vector Parameter. For the Input, type in the parameter name you used that you would like to change in your particle system. For the color, you may either hard code a color or create an editable variable that can be used. In the example above, I have hard coded the color, set the Parameter name to "color" which matches that found in my particle system, and I added a Print String node just to verify that the graph runs when I play/simulate.

In order to update all of these blueprints at the same time, a dirty method is to use the Get All Actors of Class node and then output the array through a For Each loop into the target of the Set Vector Parameter node. This should not be used as the final solution though. A note about the setup above is that it uses a Linear Color node that is converted to a vector. I did this to make selecting a color more easy without having to type in specific values when editing the blueprint instance in the level.