Armor kits are dropped often enough by enemies. The markers are white color and you will see the health icon within the beacon light. Walk over it and you will pick up the armor kit. I do not think there is any way other than this to get additional kits. You can unlock perks back at the base that lets you carry more kits at once. This is a great thing to buy if you find yourself running out of them often enough. This way you will end up picking up more of them when you dont need them and have plenty in reserve when things get tough.