I just finished that book actually. I am now reading The Gnostic Bible edited by Willis Barnstone and Marvin Meyer. In that they point to references in Sethian and Manichean Gnostic texts referencing Zoroaster the prophet, for instance in the Secret Book of John. Also, Mani proselytizing in Persia invokes Zoroaster and Zoroastrian symbolism. As far a continuous direct link, there probably is not a good way to prove that; not with out more Zoroastrian texts or more Gnostic texts.

That claim - if really that uttered that strongly (I haven't read said book) - seems a bit dubious indeed, maybe originating in a very enthusiastic approach to the importance of Zoroastrianism in a general "history of ideas" and its impact on those religious movements we call "Gnosticism". I actually know of no Historian to make that claim in such a strong manner - "Gnosticism" as a continuation of Zoroastrian dualist beliefs.

However the general notion that there was a Zoroastrian influence on some Gnostic movements was relatively often suggested. Hans Jonas, for example, distinguished two archetypes of (ancient) Gnosis - a so-called "Syro-Egyptian" and an "Iranian" one. The first category is mainly based on geographical indications and was said by Jonas to be heavily influenced by a Hellenic "dualism" (Platonic ideas) while the second one (according to Jonas) does indeed stem from Zoroastrian dualism. The first category included most of the "classic" Gnostic systems (Nag Hammadi texts (though those weren't fully accessible to Jonas yet), Valentianism, Marcionism, Hermeticism), while Manichaeism and Mandaeism are of the second type. Jonas' notion of a two-fold Gnosticism was carried on by Kurt Rudolph and found its way into his famous book Die Gnosis, which was for a long time the go-to work on Gnosticism. Both Jonas' and Rudolph's books are largely out-dated nowadays (though still worth reading, with caution of course) and the differentiation between the two stereotypical forms of ancient Gnosis is not something modern-day Historians would agree with as that's a very broad and rather useless abstraction, especially the artificial construction of the "Syro-Egyptian" type.

Manichaeism however originated in Mesopotamia and may have been influenced by Zoroastrianism to some degree, so there's some (not much) merit in the category of an "Iranian" Gnosis - Mandaeism is another problem altogether, because Mandaens are probably adherents of a Jewish baptismal community who migrated to Mesopotamia after the fall of Jerusalem, which doesn't make them very "Iranian" to begin with. Anyway, Mani grew up in a Judeo-Christian community and that's probably were he got his main influences from, but none the less Manichaeism shows some interesting similarities to Zoroastrianism that differentiates it from other Gnostic movements - the strongly emphasised metaphor of light/darkness, the preexistence of good and evil in a truly dualistic world-view (whereas "classic" Gnostic texts are only "dualistic on a monistic background", as the definition of Messina puts it - meaning that the good came first and the evil was created later "by accident" creating the dualistic antagonism). Mani supposedly wrote a book in Middle Persian, dedicated to his patron Shapur, which included a summary of his teachings in Zoroastrian guise. But that's one of the key features (and problems) of/with Manichaeism anyway - it's distinctive ability to adopt already present religious ideas in different geographical locations to make its own teachings more accessible, which means that this doesn't fight for a great Zoroastrian influence on Mani or Manichaeism. However some form of Zoroastrian influence on Manichaeism is certainly apparent though that doesn't warrant the statement made by Kriwaczek.

As /u/dantetrifone pointed out there are a few references to Zoroaster or his (legendary) forefather Zostrianos in Sethian texts. The already mentioned Apocryphon of John in it's long version (NHC II,1 and NHC IV,1) includes a rather puzzling anthropogeny of the first human who is fashioned by the evil demiurge and his "Authorities", that is angels and demons at his service, after the heavenly image of the human. Every part of the body (including senses and passions) is designed by another "Authority" and the author of the Apocryphon goes on in telling the reader that there are even more of them and whoever wants to know about them should read a "Book of Zoroaster". There's also the tract Zostrianos (NHC VIII,1) which is a rather late Sethian work with a strong philosophical approach and which contains a cryptographical colophon that refers to Zoroaster, so it has been suggested that Zostrianos is identical to the "Book of Zoroaster". Porphyrios tells us (Vita Plotini, 16) of texts written under the name of Zoroaster - among them a Gnostic Apocalpyse of Zostrianos, which is widely believed to be the treatise Zostrianos in the Nag Hammadi Codices -, which he refuted as he proved that these texts are "new" and "false" and therefore only claim to be from Zoroaster. He also mentions another "Apocalypse of Zoroaster", which we don't have, but which might be identical to the "Book of Zoroaster", if that is not to be identified with Zostrianos. Anyway, none of these works (well, those that we can actually read) are really "Zoroastrian" in their content, they use the very old and revelled names of Zoroaster/Zostrianos to give their teachings the sweet fragrance of authority and importance.

Another thought that Kriwaczek may have had in mind when writing his book is that the Zoroastrian dualism had a strong influence on Jewish apocalyptic thinking - which in return was probably one of the main influences on Gnostic movements. So one could indeed argue for an indirect, "second-hand" Zoroastrian influence on Gnostic movements. If not, I fail to see where his claim originated in and how it could possibly be defended.