Normalize Fourier Transform For Video Game
Not sure if your approach is the right path. Anyhow, hearing aid research has produced many "long term average speech spectrum" (LTASS) curves that you can use to whiten the spectrum by dividing it with the LTASS. Have a look at http://www.dydaktyka.cba.pl/AvSpeech.pdf (Byrne et al. 1994 "An international comparison of long‐term average speech spectra" J. Acoust. Soc. Am. 96, 2108) Just don't divide by the LTASS dB values but linearize them first to $10^{LTASS\_in\_dB/20}$ if you are dealing with magnitude frequency spectrum or to $10^{LTASS\_in\_dB/10}$ if you are dealing with power spectrum.

Here's the worldwide average LTASS from Byrne et al. 1994:



Freq.   Male    Female  Combined
(Hz)    (dB)    (dB)    (dB)
63      38.6    37.0    38.6
80      43.5    36.0    43.5
100     54.4    37.5    54.4
125     57.7    40.1    57.7
160     56.8    53.4    56.8
200     58.2    62.2    60.2
250     59.7    60.9    60.3
315     60.0    58.1    59.0
400     62.4    61.7    62.1
500     62.6    61.7    62.1
630     60.6    60.4    60.5
800     55.7    58.0    56.8
1000    53.1    54.3    53.7
1250    53.7    52.3    53.0
1600    52.3    51.7    52.0
2000    48.7    48.8    48.7
2500    48.9    47.3    48.1
3150    47.0    46.7    46.8
4000    46.0    45.3    45.6
5000    44.4    44.6    44.5
6300    43.3    45.2    44.3
8000    42.4    44.9    43.7
10000   41.9    45.0    43.4
12500   39.8    42.8    41.3
16000   40.4    41.1    40.7