Flies are great things, if you are using set triggers: they let the tip of the sear float over the half-cock notch. A single trigger does about the same thing by holding the sear arm up and preventing the sear tip from engaging while the tumbler rotates.
In theory (and occasionally in practice), when using a single trigger, the sear can catch in the tumbler. But muskets, shotguns, and many if not most early rifles, didn't have a fly in the tumbler, and they worked just fine.
In my case, I hadn't even considered the fly. My trigger guard won't let me use a double trigger, and since I won't have time to build a good single-set trigger, I'm just going to use a single trigger on this build. If I lose the fly, I can replace it after deer season.
But as Smylee pointed out, it is an easily lost part, and one most folks want to replace immediately if lost. My spare parts kit for my usual locks must have a half-dozen flies, just-in-case, and I'll probably order a spare for the Davis lock the next time I order parts.