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The KINDLE's Li Po battery capacity is 1750 mAh nominal (new). I believe end of life criterion is 80% capacity. All Li batteries have life time of three to five years from date of manufacture, and 300 - 500 charge-discharge cycles (1750 mAh), they have no memory or need of conditioning. The remaining capacity gauge needs occasional recalibration by normal discharge to the charge warning.
An LED is in general a high current device. A 1 watt LED may draw 250 mA at 4 VDC (KINDLE battery 3.7 VDC nominal) for 250 mAh for an hour of LED operation. Suggesting that the KINDLE battery may be able to light this high current LED for ~7 hours.
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