An AMD A10 will handle FL studio just fine. Plus, the 8970m is a great choice for light gaming while the 770m is more high end.
I think what you should be more concerned about for music production is what kind of sound hardware the laptop has. I'm not sure exactly what level of music production you are doing, but if it's high end you may want to consider an external sound card. The quality of audio capacitors, op-amps, DAC/ADC, etc. will make a difference.
Maybe something like a Focusrite audio interface would be an option.