Does Apple replace charging cords for free?

No.

Apple won't replace a damaged charging cable.

But before going out to an Apple Store to buy, yet, another charging cable from Apple, look for better quality charging cables at local electronics stores that carry Apple products OR look online from Amazon for thicker, better quality cables.

I found much better quality cables from both Belkin and Rocketfish.

Amazon has some better cables, too, from, lesser known manufacturers, but these cables do appear to be heavier duty and some are even braided for longer life and durability and some are made using a flat wire (think alfredo pasta noodle) design which is, also, more durable.

Apple's charge/sync cables, in the past, have been on the thin diameter size and don't last very long before the outside insulating coating wears enough to break open and expose the wires.

I was pleasantly surprised by the thicker and longer charge/sync cable I received with my iPad Pro. That's a much thicker cable from Apple than I am used to getting when purchasing a new iDevice. Considering the premium price I paid for the iPad Pro, that was a very welcome plus!

My iPod Touch 6th Generation, however, came with the "normal Apple standard" obligatory thin & flimsy charge/sync cable.

I use that cable just for syncing my iPod Touch and my iPad Pro to my computer to sync and backup to iTunes when I need to do this.

I use the heavier duty cable that came with my iPad Pro to charge both my new 6th Gen iPod Touch AND my new iPad Pro.

😉

Good Luck!

No, warranty is not covered by user damages.

You can buy a new one.