Question

I like to record my vocals through an amplifier to get an autotune effect from my tc helicone c1, it sounds pretty good but I'd like to know if there is any way to make the sound come through clearer and sound less distant from the mic?

https://soundcloud.com/user-862704094/after-hours

This is an example of the sound I get

Answer 1

Re-amping through an amp is going to add a little more distortion to the vocal.  All you can do is use proper good gain staging in the analog to and from the amp, making sure to minimize any of it.