Lighting with a flood is a painful thing - films are not so sensitive to the reddish light and there's not very much of it. They're mostly heaters and you will have problematically long exposures, even with direct (harsh) illumination. Expect to get at least 1 stop less sensitivity from B&W film than metered, and lose 2 stops if you use a tungsten/daylight conversion filter. And those filters assume 3600K whereas most cheap floodlights are 2500K, so you'll probably still end up with a dim orange result.

Flash is fine for children of all ages - say you shoot ISO160 and f/16, that's less than 1/100s of daylight equivalent and while that might surprise a subject it's not in any way dangerous. Any subject will quickly get used to the light (and popping sound of large strobes) if you warn them and set it off a few times. No one's pupils or eyelids can react faster than the approx 1/1000s flash duration, which is why you get nice wide pupils in studio shots.