Boost converter from 0.3 V to 12 V
0.3-0.8 is really low voltage but, on the other hand, no other info are provided therefore i assume that we can draw as many current as we wish.

Forget to do something at 0.3V but starting from 0.5V we can harvest something.
The U1V10F5 can operate from 0.5V, with a max current of 1.2A. The output voltage is 5V, and the efficiency is between 70%-90%, we can assume 70%. 

1.2A @ 0.5V are 0.6W in input, considering the efficiency we have 0.42W at the output.

From 5V we have to increase the voltage again, the U3V50F12 will increase the voltage up to 12V with the highest efficiency i've found so far in the pololu catalog: 85%-95%. We assume again the worst case, it won't be far from that in reality.

0.42W x 85% = 0.375W
0.375W @ 12 = 0.03A (approx)

I don't get why you want to use a linear CC charger with only 30mA of available current, for a NiCd battery pack, which is one of the most resilient cell chemistry.

Edit: now that you attached your diagram this answer doesn't add much except few considerations on the current. You are considering only the voltage.
To have 250mA at the LM317 input you'd need, assuming 80% efficiency in the LM (which is not really conservative, imho), more or less 9A @ 0.5V.
Are you sure that your power supply is anywhere near this spec? (not to mention the unavailability of pololu converters that can handle this much current)