The strength of the Earth's magnetic field affects the amount of cosmic rays entering the atmosphere.
However, even with such historical calibration, archaeologists do not regard C produced and therefore dating the system.The amount of cosmic rays reaching the Earth varies with the sun's activity, and with the Earth's passage through magnetic clouds as the solar system travels around the Milky Way galaxy.It cannot be used to date volcanic rocks, for example.The rate of decay of N in 5,730 years (plus or minus 40 years).So, we have a “clock” which starts ticking the moment something dies.
Obviously, this works only for things which were once living.
Since the flood was accompanied by much volcanism (see Noah's Flood…, How did animals get from the Ark to isolated places? ), fossils formed in the early post-flood period would give radiocarbon ages older than they really are.
In summary, the carbon-14 method, when corrected for the effects of the flood, can give useful results, but needs to be applied carefully.
Clearly, such huge time periods cannot be fitted into the Bible without compromising what the Bible says about the goodness of God and the origin of sin, death and suffering—the reason Jesus came into the world (See Six Days? He said, This only makes sense with a time-line beginning with the creation week thousands of years ago.
It makes no sense at all if man appeared at the end of billions of years.
Unless this effect (which is additional to the magnetic field issue just discussed) were corrected for, carbon dating of fossils formed in the flood would give ages much older than the true ages.