The following code:

        String[][] ss = {{"a", "b"}, {"c", "d"}};
        Stream.of(ss).
                flatMap(Arrays::stream).
                takeWhile(
                        e -> e != "c").
                forEachOrdered(System.out::println);

will output:

    a
    b
    d

takeWhile is incorrectly assuming that an upstream operation supports and honors cancellation, which unfortunately is not the case for flatMap. (It's tricky to support given flatMap operates on a public Stream whose implementation may not be known. forEach variants supporting cancellation is required).

The current implementation of while op Sink::accept is:

                    @Override
                    public void accept(T t) {
                        if (take = predicate.test(t)) {
                            downstream.accept(t);
                        }
                    }

it should be:

                    @Override
                    public void accept(T t) {
                        if (take && (take = predicate.test(t))) {
                            downstream.accept(t);
                        }
                    }