I know that when my former boss, who is now 78 years old, was a kid doing combustion controls, the flame rods were made from Kanthal. It's been around for awhile.
Kanthal is made from iron, chromium and aluminum and has a higher temperature rating that its competitor alloy nichrome (80% Ni, 20% Cr).
I'm guessing that an alloy of iron and aluminum is cheaper than one with a very high percentage of nickel and some chromium, and that for the service involved with a flame rod, that Kanthal is the best material with the longest service life available.
Here's Kanthal's sales brochure comparison of Kanthal to nichrome:
I wasn't aware that any combustion control flame rod electronic control 'calibrated' to a stainless steel flame rod. I'm guessing that if the SS conducts the rectified current well enough to hold the flame safety relay "in", that SS would work, but why would you not use a material that's been accepted as an industry standard for so many decades?