By following the Bugzilla post, given by jbkt23, I got it to work easily using a workaround of the buggy memcpy function.

So I decided to write down the steps needed to get it to work according to this post: https://bugzilla.redhat.com/show_bug.cgi?id=638477

1. Open your favourite text editor and paste this text:

#include <sys/types.h>

void *memcpy(void *dst, const void *src, size_t size)
    {
void *orig = dst;
asm volatile("rep ; movsq"
  :"=D" (dst), "=S" (src)
  :"0" (dst), "1" (src), "c" (size >> 3)
  :"memory");
asm volatile("rep ; movsb"
  :"=D" (dst), "=S" (src)
  :"0" (dst), "1" (src), "c" (size & 7)
  :"memory");
return orig;
    }

2. Compile it:

gcc -O2 -c mymemcpy.c

3. Make the .so file:

ld -G mymemcpy.o -o mymemcpy.so

4. After that you can launch Firefox/Chrome with the new memcpy using the fallowing commands:

Firefox:

LD_PRELOAD=<full path to mymemcpy.so> /usr/bin/firefox &

Chrome:

LD_PRELOAD=<full path to mymemcpy.so> /opt/google/chrome/google-chrome &

By now your flash should work normally, but as starting your browser always from the command line using this long command can be a little annoying, I added two more steps:

5. Copy your mymemcpy.so to some system directory, like /usr/lib64, so it is accessible to all users.

su -
cp <full path to mymemcpy.so> /usr/lib64

6. Edit Firefox startup script:
Use your favourite text editor and open file /usr/bin/firefox. I used nano, but any other will do:

su -
nano /usr/bin/firefox

Now find a last comment line (## mozilla work.) and insert this text right after it:

export LD_PRELOAD=/usr/lib64/mymemcpy.so

Save and close your text editor. Now you can run your Firefox by just typing "firefox" into the command line or double-clicking on the Firefox's desktop icon like usually.
Probably you have to repeat the last step after you update Firefox, as the update process will probably overwrite the /usr/bin/firefox script.