[dom123dom]

Looking at the datasheet here: https://www.rohm.com/datasheet/BD71815AGW

I can see what you mean it talks about:

Embedded Coulomb Counter for Battery Fuel
Gauging
- 15-bit ΔΣ-ADC with External Current Sense
Resistor (10 mΩ, ±1% or 30mΩ, ±1%)
- 1-sec cycle, 28-bit accumulation
- Coulomb count while charging/discharging

and

15-bit ΔΣ-ADC measures the battery’s charge and discharge current by means of an external current sense resistor
(10mΩ, ±1% or 30mΩ, ±1%).

So should it be 10mΩ or 30mΩ for the Kindle? You mentioned 30 above.

Is this the right one?
https://www.digikey.com.au/product-d...RCT-ND/2003876

EDIT:
With a magnifying glass I can see 030 printed on the chip so I just bought the ones below, I hope they are the right model!
MCS1632R030FER - Ohmite - Current Sense Resistor

I think this will be very challenging soldering for me, it looks tiny.