It's not that I know too much about it either, I'm just studying it, so got a chain of thoughts in my mind, I still have a long way to go :)

1. The required unit of chronal potential ${\varphi }_t$ would be $\frac{s}{kg\cdot m}$
   If we accept these units for the chronal potential, it means:

Chronal potential is a measure of how time flows per unit of momentum-space displacement.

It inversely scales with mass and position, implying heavier or faster-moving objects dampen the local time flow (sounds heretical to Minkowski and Schwarzschild metrics)

2. Oh maybe I didn't explain properly, thanks to that, I got caught up in the thought and forgot to define chronal field vector

$\vec{C}=-\nabla {\varphi }_t$

so it becomes

$\Delta t=\vec{C}\cdot |(\vec{T}\times \vec{p})|$

so maybe,

$\Delta t={\int }_a^b\vec{C}\overrightarrow{dl}$