The first ability of Conqueror’s Flail constantly updates as the number of colors among permanents you control changes. If the number of colors decreases and the damage that was marked on the equipped creature earlier in the turn is now lethal damage, that creature is destroyed. Similarly, if its toughness becomes 0, that creature is put into its owner’s graveyard.
If you move Conqueror’s Flail from one creature to another, there’s no time in between that it’s not attached to a creature. Assuming it’s your turn, your opponents won’t be able to cast spells.