As of now, I'm stuck troubleshooting the whole thing. If anyone knows about USB C, please help out with your suggestions.
When I plug the device into the phone, keyboard always lights up (ie the chip is powered), the phone either detects it as a keyboard, or as a device charging off the phone. More often than not, the latter one is what it is detected as and therefore the keyboard does not work at all. I have no idea at all what is going wrong at this point. As I said, there is power going to the chip (and the chip itself consumes very little). I've checked the data lines and they're fine as well (no resistance other than 22 Ohm for each line as suggested by the manufacturer). This problem repeated itself with both chips (one in the test rig and the other one in the prototype slider) and the chip works fine when I plug it into a regular computer.
I feel like there must be some technical detail (regarding USB in General and USB C in particular) that I'm missing out on. And the fact that the fault is intermittent, makes the fault that harder to trace!