I am using the MIC29300 https://www.microchip.com/wwwproducts/en/MIC29300 in my circuit to generate a 5V signal to my ADC (works fine now)
Would it be possible to grab that 5V line and have it provide the power for my Raspberry Pi 3 Model B+? Would it cause voltage fluctuations and affect my ADC? Should I just use another IC?
You COULD use a linear regulator if you have a large enough heatsink because any linear regulator will dissipate lots of heat.
Whether the voltage would be stable and sufficiently clean depends on the circuitry you put around the regulator.
I wouldn’t use a linear regulator switch mode power supplies are preferable.
PS I don’t know why you would want to use a separate regulator with an ADC – most have precision internal references, which are temperature stabilised.