I'm NOT trying to bash anyone here, but I think flashlights on dark rides is a TERRIBLE idea. The rides are dark for a reason, maybe to create an atmosphere, maybe to hide some of the workings of the ride so as to create/preserve "the magic," and most likely a combination of both.
It seems to me that light from a flashlight would alter the atmosphere and also make visible some of the should-be-invisible stuff that helps make things look cool.
I know that flashlights aren't as bright as photographic flashes, but I have to say, someone rudely taking flash pictures during a performance of the Voyage of the Little Mermaid really ruined the magic for me, and it still bothers me 3 months later. It made visible how those wonderful colorful characters floated and swam, and badly detracted from everyone else's ability to suspend their disbelief and enjoy the magic and wonder of the show.
I have a 6 year old and 4 year old. But I wouldn't prioritize their comfort over potentially ruining or lessening the experience for everyone else. It would be an inadvertantly selfish thing to do, IMHO.
The glow bracelets suggestion sounds PERFECT. Provide the child a sense of security while not throwing light on anything and thus not taking away from anyone else's experience.