Using fat to power portable electronics makes a lot of sense
 

Fat is about 50 times as energy dense as the best lithium batteries. Even if the conversion efficiency were only 10%, that's still a good 5 times advantage.

So as it turns out, the obesity epidemic could well be the solution to powering portable electronics. There's already a product out there that does it:
Charge your phone using pedal power with the K-TOR Power Box
The obvious flaw is that while it's reasonably easy to generate 50-100W with a pedal generator, most tablets only accept charge at 10W or less. They also expect a very stable supply so something like a laptop (which can accept as much as 90W) won't charge properly. That's probably why that device is limited to only 20W, in order to account for inrush.

Maybe the solution is to develop something like that but with a built in high current battery. Then it's just a matter of a 30-45 minute workout in order to charge your device for a few hours.

Back when I worked at Intel, their gym had some rather interesting stationary bicycles with USB ports for charging your smartphone. (I don't think it has a built in battery.) So the idea works, we just want it in a more portable form factor.

I agree, a small LiPo battery would allow you to store that power and use it whenever you want.

you can use circuity to condition the power so you can have a 5v continuous output. If you hook a DC motor to a gearbox that ramps up the speed you can get some good voltage. Just add a couple large capacitors and a five volt voltage regulator and you have a cell phone charger. The capacitors will help smooth out the spikes and the voltage regulator will convert a wide range of voltage to a continuous 5 volts. I believe as long as you generate at least 8 volts the regulator will output 5 volts.