For the flash measurement, 1/250 is not relevant. A flash meter tells you ONLY the aperture because the flash duration is (much) shorter than your shutter speed; the only constraint being that if your camera has a focal plane shutter you need to stay under the X-sync speed.
Like Ralph says, you pick an aperture that's "suitable" for your flash, i.e. places the flash exposure at normal, -1 or whatever, and after that, you select the shutter speed to get the lighting ratio you want. Or you pick a shutter speed due to some other constraint (moving subject, whatever), that tells you the aperture and from there you adjust the flash power.
A common configuration is sun for "normal" exposure and flash at -1 for fill. Say you're shooting ISO100, a likely combination would be f/11 1/200s exposure (sunny-16 light) and the flash with enough power to illuminate f/8, i.e. one stop less than what your aperture is actually set to. If you wanted the flash and sun to be equal, obviously you'd set the flash power to f/11 but it's going to look bright & flat and if you're shooting chromes then you'll actually be a stop overexposed on any part of the scene that is lit by both sun and flash. If you want more DOF (smaller aperture) with the same lighting balance, you need both a longer exposure and more flash power.
Aperture affects both flash and ambient, shutter affects only ambient. Flash/subject distance also affects flash power via the inverse square law, so a little bit of moving stuff around can go a long way.