Be sure your Fitbit Flex USB charging cable is plugged into a USB port, your computer is ON and not in sleep mode.
The arrow on the actual Flex Tracker should face down in the charger with the charging terminals toward the inside of the charger.
You should see the LED's illuminate every 5 seconds or so showing the charge level while it is charging. If you do not see this, try pushing the flex tracker into the spring loaded terminals with a little pressure while it is plugged in. If you see the LED's illuminate when you do that, there may be a poor connection between the Flex Tracker and the charger. You may need a new charger cable. Using a rubber band around the Flex Tracker and charge housing to hold pressure against the charging terminals is a temporary workaround.