Will this design for an XHP70.2 LED Driver with arduino control work to the params specified?
You need to compute some common-mode and differential voltages.

I use 50mV for max current to choose the current sensor.  For smaller power you might be able to use say 20 or 25 mV FS but your R ratios need to be low error 0.5% or better have matched gain ratio arrays for high CMRR noise rejection.  Note: Very layout sensitive for high gain. And logic loops on schematic need to be physically as small as possible with stray inductance and high gain. (~100~200)

Then use R4/R2=R3/R1 for gain.  Check Vcm min~max to make the inputs within Rail-to-Rail or else move the sensor to the ground side of the load and choose any dual PNP input Op-Amp to sense near 0V.

The next stage might use equal R values for unity gain.