We've already seen that there were lots of ways out for individual Amalekites who wanted to run away. We have seen that the primary intention of God's command in 1 Samuel 15:3 is to stop the Israelites profiting from the destruction of the Amalekites. But given that command what about children who remained? Would they have been killed?
Probably, yes. And that's hard to say.
But think about the situation. We've seen that the Israelite army was huge and slow-moving - that there was plenty of time for people to get away. Whose fault is it if children stay behind for a battle? Whose fault is it if a parent takes their children to war and the children get killed?
It's the parents' fault, isn't it? Let's take an example from WW2. Just before the D-Day invasion, the Allies parachuted troops into France to secure vital bridges and so on. The normal orders for such troops is to take no prisoners, just like for the Israelite army. Now suppose they are faced by a column of German infantry, and the column includes women and children, who are also fighting. Whose fault is it if those children die? Is it Churchill's, for ordering that the troops take no prisoners? Or is it their parents' for making them fight when they should be keeping them safe?