How to safely wash a Nomex flight suit?
Firstly to clarify:

What are the differences between “inherent” and “treated” flame resistant fabrics?
Inherently flame resistant fibers are materials that have flame resistance built into their chemical structures. Aramid fibers from companies like DuPont create inherently flame resistant fibers, with brands such as DuPont™ Kevlar® and DuPont™ Nomex®.....

With that information:

Laundering’s impact on flame resistance
An essential thing to keep in mind when assessing flame-resistant technologies is that inherent flame resistant properties cannot be washed out or damaged through exposure to chemicals in the workplace or laundering practices, whether at-home or commercial.
FR-treated garments, however, may be damaged by chlorine bleach, the combination of hydrogen peroxide (“oxygen bleach”) with hard water, or exposure to oxidizing chemicals in the workplace. Source

An extensive DuPoint Nomex Laundering Guide
For the 'treated' fabrics, reading this DuPont document might be interesting.