How large a span can a 4x6 hold safely for a swing set.?
Looking at span charts, such as http://www.southernpine.com/app/uploads/AL_33-38L.pdf
I see the Total Load for a plywood covered angled roof from SYP is as low as 34 lb/ft for a 2x6, and doesn’t simply double for a 4x6.

You are talking about a clear span of nearly 16’ with a total weight up to 400lbs swinging back and forth exerting greater than your listed weights when swinging hard — I think you’d want much closer supports and a lot of extra bracing. You might not immediately break the beam, but I can see it flexing a lot, and possibly pulling down the sides, especially if they are not attached to rigid anchors at the ground. From wood, for that type and use of span, I think you should look at a laminated, engineered beam.