Here is a rambling set of resources/publications I have collected on the topic.
I haven't dug into any of them enough to give real firm advice about whether or not they can be performed in R. The Flow mapping software and the Hennemann articles use slightly different and novel techniques (so I'm guessing would take custom code), the Ratti article though just looks like it uses some regular definitions from other networking theories (the Hennemann and Guo articles take some pain to make sure the clustering obeys spatial configurations).
Those articles are about clustering regions of inter-connections rather than clustering flows (which it sounds like you want), but some articles on clustering the flow lines themselves exist. For an example see Phan, Doantam, Ling Xiao, Ron Yeh, Pat Hanrahan & Terry Winograd. (2005) Flow Map Layout. In Information Visualization, 2005. INFOVIS 2005. IEEE Symposium: 219–224.| PDF here You can see similar interactive layouts in the D3.js hierarchical edge bundling, or here is a really cool example of it as well, Global Dependency Explorer via visual complexity. Unfortunately D3.js does not appear to support native flow data like you have, but may be something to keep on the radar (if that is something you want).