If asked questions about other minds, how would/does he respond, and does/would he nest his response in physical science and reductionist/determinist models? Does he say that their existence is easily demonstrated? Doesn't need to be demonstrated? Other?
Dawkins shows every sign of being a (philosophical) realist and resisting attempts at philosophical complication of empirically robust results. (If pushed, I'm pretty sure he'll follow the data: "the best model is that reality is 'real'".)
Therefore, he would, I imagine, say that we have oodles of evidence that our minds are all quite similar; whether or not it's easy to demonstrate, we have so much evidence that it is easy to draw the conclusion.
If you come up with some weird philosophical construct that raises doubt that there are other minds, Dawkins would likely respond with: is that parsimonious? Is that predictive? Does it have explanatory power? (And probably a few choice words of a less polite nature making clear that he doesn't think much of the process that makes one take such a proposition seriously in the face of so much evidence.)