Do National Fire Protection Association standards apply to the US Army?

Not directly. The military has its own fire regulations, which may be based upon NFPA standards, among others.

For example, military regulations may have different hose threads for fire engines used at military installations, compared with what local civilians may be using.

Planning and inspections may also be completely different from what NFPA requires, although federal offices within commercially leased spaces may still be subject to all local codes as well as federal (military) regulations.