The battery won't be flexible. You can have multiple batteries with flexible connections but they'll be a likely point of failure. Will you really need that much power? Bluetooth LE really is "low energy" as are many sensors. If it's supposed to make a lot of light, noise, has a motor, or use more powerful RF like WiFi, then the power requirements will be greater.
You've already be directed to Adafruit which is a great resource, not just as a store and product developers in their own right but for all their learn materials and years worth of weekly videos. Here's a breakout board for charging their little LiPo batteries via MicroUSB.
You've already be directed to Adafruit which is a great resource, not just as a store and product developers in their own right but for all their learn materials and years worth of weekly videos. Here's a breakout board for charging their little LiPo batteries via MicroUSB.
https://www.adafruit.com/product/1904