The documentation for IO::Compress::Zip marks Append with the Functional Interface as TODO. I tried your example using the OO interface with Append (the doc implies that should work) but got no further. However Multi-Stream seems to work:

#!/usr/bin/perl
use strict;
use warnings;
use IO::Compress::Zip qw(zip $ZipError :constants);

my $z;

$z = new  IO::Compress::Zip  './k.zip',
  name        => 'from_filename.t',
  AutoClose   => 1,
  BinModeIn   => 1
        or die "IO::Compress::Zip(1) failed: $ZipError\n";

open (my $fh, '<', './a.txt') or die "Unable to open a.txt: $!";
while (<$fh>) { $z->print ($_) }
close $fh;

my $string = ss();

$z->newStream(
  Name       => 'from_ram.t',
  ExtAttr    => 0666 << 16)
        or die "newStream failed: $ZipError\n";

$z->print ($string);

close $z;

sub ss {
    return <<END;
a
b
c

END
}
[download]

Note that I set the permissions in ExtAttr - the default does not appear to be implemented (I got 000 without it), and it is not a string as your code supplies it.