I prefer reusable idioms.

Here not is indeed more readable, but it won't produce 0 for false, which could be counterintuitive in other cases.

$flipflop needs to be declared, while $a (and $b) is already global as part of the sort idiom, which is a similar case of using a code block.

$a=1;
my @result = grep { $a = not $a }, @input;
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At the end it's a matter of taste. ^= is shorter, = not is clearer, but =1- can equally be used in most other languages, making it an universally understood idiom.