You can use a Navigation widget to do this .Just put this widget on your mashup and assign the mashup(In Navigation widget property settings "Mashup Name") to which you want to redirect after double clicking on your chart .you can also mark it not visible if you do not want to show this (Again from "Visible" setting in Navigation widget property ) .Now map "double click" event of chart(this is an event in chart widget property settings) to this navigation widget .
There is also an option for "Target Window" in Navigation widget property settings from where you can decide whether you want to redirect to new mashup as a new window or in same window and many more options are there .
I have also similar requirement, I am trying to click on Label chart graph, I have put the navigation also so that it takes to me new mashup and it is working fine. but main problem is that I need to double click on bars of that graph only then only it will take to new mashup, If you click on any area on that graph or on that widget it wont take you to new mashup. is this designed like this in thingworx or any other possibility will be there.
There is a common, tricky & fast (not best practice) workaround.
If your labelchart is in the panel or similar container you can add widgets, which will overlay existing ones in mashup.
In my example I added new button which has DefaultContainerStyle as a style and put it on the Label Chart.
Now you can see that it is not visible but still clickable so you can use it as a dummy Click Event on Label Chart.