What kind of lens flare would a binary star-system produce, provided we could see them with a typical camera?

I've been working on an illustration of a canyon under a binary sky, and I wanted to add a lens flare effect to make the shot seem more like it was taken with a camera (it adds a sense of realism to an otherwise two-dimensional piece of artwork), but I'm unsure how to go about doing that. Assuming the stars are naturally twins in size, but one appears closer than the other, how would a flare appear on the lens? Would it be two lens flares perpendicularly bisecting each other, or would some other effect be produced?