If I shined a flashlight into the sky, would someone in another galaxy eventually see it?

Not at all.

The trillions of photons emitted by your flashlight each second would expand into space and become more dilute according to the inverse square law. By the time they got to the top of the Earth's atmosphere, there would be fewer than one of these photons per square meter. They would get washed out by the local production of optical light by our atmosphere, and then merge into the stream of light emitted by the Sun...which is enormous!