use strict;

my $Kine = "Hello, FLF12. Would you like to play FLF22?";

# I've substituted array refs for the SQL query. It's
# approximately the same as the 'while' line you have.
foreach my $row (["Dr. Falken", "a game"], ["Bobby Fischer", "some chess"]) {
   my @Replacement = ();
   $Replacement[12]=$row->[0];
   $Replacement[22]=$row->[1];

   $Kine=~s/FLF(\d\d)/$Replacement[$1]/ge;
   print $Kine, "\n";
}