Does MapPoint, or any of its add-ons, have the capability to display flow from one point to another? I am looking for lines between points whose width is proportional to amount of flow.

Example, I would like to import 10 locations and the amount of traffic that flowed between all possible pairs of those 10 locations. I would like to see a network diagram with straight lines between all the pairs with their width scaled to the amount of flow.

I have seen these maps drawn before, but dont know what software is able to do it.

If not MapPoint, what other mapping software could do this?

Presumably you have location information for each of the points (nodes). MapPoint could take latitude,longitude coordinates, or address information (including a simple city + state/county/whatever).

You are also asking for straight lines which makes it relatively easy to code up. You would load the node data, convert these to location objects.
Perhaps plot a pushpin for each location if required (optional).
Then load the link (flow) information. Then for each link, a line is drawn between the two relevant location objects.

I think MapPoint has only a limited range of line thicknesses, so this should be borne in mind. The link colour can be changed as well, so this could increase the number of combinations available.

Depending how urgent this is, I could be hired to write this for you...