Use a buffer.

[how do I ensure that I don't messages] off midway in between reads?

When you've found a message, add to the buffer until you find the end of message.

how do I ensure I don't save the same messages twice?

Remove them from the buffer as you process them.

how do I ensure that I don't skip any messages

I don't see how that could happen.

Untested solution:

my $BLOCK_SIZE = 64 * 1024;

# Until EOF,
for (;;) {
   # Read a chunk.
   my $rv = read($fh, my $buf='', $BLOCK_SIZE);
   die  if !defined($rv);  # I/O error.
   last if !$rv;           # EOF

   # For each message in the buffer,
   for (;;) {
      my $pos = index($buf, "\0\0Msrc");
      last if $pos < 0;

      # Discard the uninteresting bits.
      substr($buf, 0, $pos, '');

      # Read the header.
      while (length($buf) < 22) {
         my $rv = read($fh, $buf, $BLOCK_SIZE, length($buf));
         die if !defined($rv);  # I/O error.
         die if !$rv;           # Incomplete message
      }

      # Discard the header.
      substr($buf, 0, 22, '');

      # Locate the end of the message.
      my $pos = 0;
      for (;;) {
         $pos = index($buf, "\0", $pos);
         last if $pos >= 0;
         $pos = length($buf);

         # Read a chunk.
         my $rv = read($fh, $buf, $BLOCK_SIZE, length($buf));
         die if !defined($rv);  # I/O error.
         die if !$rv;           # Incomplete message
      }

      # Extract the message.
      my $msg = substr($buf, 0, $pos, '');

      # Process the message.
      do_something($msg);
   }
}
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Others ([1] [2] [3] [4]) have assumed the amount of data between messages is rather short. My solution makes no such assumption.

Update: Added answers to direct questions.
Update: Added note concerning assumptions.