What is the purpose of a voltage divider in a flex sensor?
If you have a good voltage source (you do) and you apply it across the flex sensor, the voltage will not change. The current will change as a result of the changing resistance of the flex sensor.

So if you measure the voltage across the flex sensor, it will never change. By forming a voltage divider, you can get an equation that relates the resistance (partially as a result of flex) of the flex sensor to the voltage read across it.

This in turn lets you read the amount of flex! Remember: V=IR. If V is always 5 volts, as R goes up and down, I will change to make the equation hold.