Ok...
The computer architecture evolved from 8086... 4x86... Pentium... II,
III, IV, but the core is the same.
When Fedora Developers compile the Linux Kernel, they choose a
compatibility level.
As "default", they choose i686, that is a nick-name for Pentium Pro,
Via C7, Athlon XP, Pentium II, III, and so on...
It gives a loot of compatibility.
The problem is that YOUR Fedora has (or is trying to do) 2 kernels, of
same version, installed.
One for i586 and other for i686.
Pentium VS Pentium II/Pro/Intel Core/Core 2
Try a "uname -a" to know the version you are running.
I heavily SUPPOSE that you have the i686 installed, and that yum is
trying to install the kmod-fglrx for i586 creating a false obligation
to install the i586 kernel. Only the kmod meets the kernel arch - the
binary driver will be i386.
it may be related to yum-fedorakmod package.
But without your "uname -a" output, I can't say something 100% right.