So, let me see if I have this right. You have a power source that puts out 10mV at some unknown current, and you want to boost (not amplify, that is a different thing) this power to 5V to charge a phone.
When you boost a voltage, you diminish the current by the same factor (actually more since 100% efficiency is unachievable). So to get the standard charging current of 1A you would need 500 Amps from your 10mV source, which I suspect is a wee bit higher than is available.
And typically, boost circuits don't work much below 1V. So we are getting into the area of energy harvesting (look it up). This involves accumulating the energy from a low power source over a long time to then use it in a burst for a short time. This allows you to power something that the original source is not able to power directly. For example, if your 10mV source produced 1 A (which is probably still way high), then you could accumulate the energy from it for 1500 hours in order to be able to charge a phone at 1A for 3 hours.
Good luck with your project.
Bob