While I agree it's impractical, it's not so much because of the 5V requirement. There's plenty of 5V boost regulators that require only a few external components (the inductor would be the biggest impact if there's no physical space for it in the body) and a future, or third party, revision of board could add that.
Getting that power out to your phone is the biggest problem. As it is, there's only the 1 microUSB port - getting that to serve a dual purpose would require various design changes and, depending on how tolerant other devices are, diligence on the side of the user (e.g. if you plug the Flex into your computer, how happy is it going to be when it's suddenly seeing something trying to force a 5V potential across?) So usage-wise, you'd want a second port, and then the most common is the USB A receptacle, but how/where are you going to fit that in? etc. etc.
The boosting is the easy part :)
Since David already mentioned a portable charger, I'll throw a suggestion in as well: http://www.ebay.com/itm/390516382151 . It's cheap, fairly compact, accepts 3 18650 batteries (same as the Flex, and plays with well 19670s whereas in others they might not fit), will charge 1/2/3, will charge other devices off of 1/2/3 and while there are some minor design issues, you could do worse. It is an extra device to carry, but may be a decent alternative.