Thanks for the feedback on the Anker charger with the T100TA + phone. I use $2 retractable cables from China that I get on eBay... sounds like you may have just had a bum cable.

Did you try the retractable cable with the Samsung charger? I've had issues with my kids' Galaxy Tab 3s being VERY picky about both non-Samsung chargers and any cable with circuitry in the path (i.e. generic micro-USB docks), but they don't seem to have any issues with the retractable cables as long as they're used with the original Samsung chargers.

I used the "Galaxy Current" app to measure current on my Galaxy Tabs and S4 when still using TouchWiz, and Elixr after installing a GPE ROM on the S4 and also on my Moto X 2014. You'll want to note that Elixr monitors the net current, so it's display what the charger is providing MINUS what the phone is drawing... make note of what it's reading prior to plugging up to get a good idea of what current you're drawing from the charger/cable.