Summary
The support staff at Digi confirms that to enable Hardware/Software flow control for their Acceleport RAS series multi modem cards, we need to pass '&K6' in our init string.

We start with our default init string:
AT&FE0V1&C1&D2S0=0

Now we add '&K6':
AT&FE0V1&K6&C1&D2S0=0

For FaxMan Jr., we need to set the control's DeviceInit Property:
FaxManJr1.DeviceInit="AT&FE0V1&K6&C1&D2S0=0"

For the FaxMan SDK, we can set the init string either in code (FaxMan1.DeviceInit="AT&FE0V1&K6&C1&D2S0=0") or via Faxman's FM3032.ini file.

[Port1]
Send=1
Receive=0
Class1=0
Class2=1
Class20=1
Init=AT&FE0V1&K6&C1&D2S0=0
Reset=AT