You misread. The theory is that the magnetic forces that create solar flares are driven by an iron core -- not that the flare itself is made of iron.
Not really, just mis-stated. I am not a friggin scientist.
If the flare was initiated by a iron cored sun, then their would be some evidence of iron someplace, somewhwere.
If, this theory is true then all suns must be similar and all solar systems would be iron based.
We just don't se any evidence of that, but what we do see is that hydrogen appears to be a major building block of stars.
We don't see iron as a sun core because it's gravity and mass as measured and known to us, do not reflect this fact.
I have never heard of this theory until now. It appears to be very unusual on it's face.
I will defer to the experts to blow holes in it.