I downloaded this mod, and I noticed then its in FOMM.

How does this work? Do you keep it checkmarked at all time?

Do using the mod conflict with Fomm own form of it?

Either one works the same, don't worry about conflicts. Archive Invalidation Invalidated isn't a mod, it's a utility that when toggled allows user made textures to show up n the game instead of a big red arrow. You really only have to use it after you install new mods that add textures and you get a big red arrow in the game. If you have FOMM, just use that one as it's the easiest.

So...click it everytime I add a new mod? Keep it checked mark aftering redoing each time?

If you're using FOMM, there's no reason to have the standalone version. FOMM already takes care of all that as it has Archive Invalidation Invalidated built into it. That will save you one more slot in your load order.