IIRC there is no g mode modifier only ixsm mode modifiers (granted there is a /g option for the regular expression, but that is different). Anyhow here is one solution (semi-tested):

use strict;

sub make_regex_list{
  my @regexes;
  foreach my $strings (@_) {
    my($regex_string,$options)=@$strings;
    push @regexes,qr/(?$options)$regex_string/;
  }
  return @regexes;
}

my $string = "Jack Jack John JACK john";
# in real code this array would be constructed
# from a file
my @reStrings=(["jack","ig"],["john","i"]);
my @REGEXES=make_regex_list(@reStrings);
foreach my $regex (@REGEXES) {
  #check to see if the regex contains the g modifier in it;
  if ( $regex =~ /^\(\?-xism:\(\?[^g|\)]g.*?\)/ )
  {
   $string=~s/$regex/name/g;
  }
  else  #no g modifier in $regex
  {
    $string=~s/$regex/name/;
  }
}
print $string."\n";

__END__
E:\>237215.pl
name name name name john
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-enlil