Imo, he supposed to be an Edo with unlimits chakra? Kishi has been trolling this lately since Minato arrived to the battlefield.
Edos only have a constant regeneration of chakra. Not limitless chakra.
So an edo can run out of chakra. Its just they will regenerate it. And they will be able to do that forever, until they are released from edo form.
Chakra actually works just like it does on ultimate ninja storm. You have a chakra bar. When you use jutsu and stuff, you deplete the chakra bar. You still have to do the action of molding the chakra(holding y or triangle).
So the edo being out of chakra is something that can happen.
Him being in kcm is where it is tricky. It could very well have been a mistranslation, and minato actually said"im low on chakra" which certainly can happen in kcm(though it normally wont)
Most likely it was just a error on kishis part. Minato probably was meant to be in base mode if he said he was out of chakra.
But honestly I dont care. I just speculate and theorize on everything. My opinion as to why minato didnt use sage mode earlier, is because he couldnt use it in kcm. And that he didnt need to use it, as he wasnt really fighting, and naruto was doing the sage mode and fighting. But unless kishi says something, this is just a speculation.