It isn't the quoting exactly. Removing the newlines in the quoted strings makes it work too.

$ perl -MTie::FlipFlop -le 'tie my $f => Tie::FlipFlop => ("white","bl
+ack"); print qq[$f]; print qq[$f]; print qq[$f]; print qq[$f]'
white
black
white
black
[download]

It isn't the platform, it's the version. I did my testing with 5.6.1 on Solaris and reproduced your results. This bug appears to be fixed in newer versions (5.8.0) of perl.

-sauoq
"My two cents aren't worth a dime.";