The datasheet for TL431 limits it to 100mA and 1kHz.
The description of your amplifier IC tells how it can attain 400mA or so. Unless my understanding is wrong, the same Ampere level has to go down through the negative supply rail, and at any frequency possibly up to 10GHz. Application schematics show TL431 operating in positive territory, never negative. TL431 does not seem adequate for the job.
There are negative voltage regulators such as LM337, 7805, etc. Some are adjustable.