You can connect the FLORA to your computer via USB. Use Adafruit's Arduino app to load sketches onto the FLORA - check out the Flora tutorial for all the details. The NeoPixel example strandtest is a great demo sketch to test the LED strip. Now you can attach the LiPo battery to the FLORA. Make sure to switch the onboard power switch to ON before trying to power the strips.
You can hook up the LED strip to the flora micro-controller with alligator clips. Wire up a red alligator clip to the 5V pin of the strip to the vbat pin of the FLORA. Next, use a black alligator clip to the ground(GND) pin of the strip to a near by ground(GND) pin on the FLORA. Now use any other colored alligator clip to pin D6 of the FLORA to the DIN pin on the NeoPixel strip. Now you can switch on the power to the FLORA to test the NeoPixelStrip. You should see LED glowly goodness, if not, don't worry! Just double check your alligator clip connections, the leads on the strip are tiny, so make sure the alligator clips DO NOT TOUCH or it wont work!
In the image below we show it with a single Neopixel, not a flexy strip, but the wiring is the same, VBAT to +, GND to -, and D6 to DIN