Think about it - if a photon (a quantum of light) can interfere with itself, why couldn’t two photons, or a million, interfere with one another? This is one of those cases where light acts like a wave - when the peak of one wave is at the same place as the peak of another, the overall effect is a bigger wave. When the troughs align, you get a bigger dip.
The reason you don’t see it with two flashlights is that they are emitting white light - or something close to it, anyways. There are so many different wavelengths of light coming out of each flashlight, and the waves of the one are not necessarily in phase with the other, so the overall effect is that you don’t notice a discrete interference pattern - you basically get a continuous amount of light, although two flashlights shining in the same spot do seem brighter, don’t they?
The slit experiment, if you do it with a single light source and two slits, will give a diffraction pattern in which the light coming from one slit interferes with the light coming from the other. This is two beams interfereing with each other, as in your OP.
As for pointing two light sources at one another, I suppose if you knew the exact wavelength of light (say, of a laser) and calculated the distance between the sources, you could get them to interfere with one another…but I don’t know how to measure that.
I’m really not that much of a physicist, I just know as much as I just said (and I hope I even got that right!)