The Shulhan Aruch (O.H. 291:4) writes that reciting Kiddush is not obligatory for Seuda Shelishit. Rabbi Shalom Messas (Shemesh Umagen, vol. I, § 65), quoting his uncle Rabbi David Messas who in turn quotes Sefer Tikune Shabbat, writes that the words “Yayin” (lit. wine) and “Gog uMagog” have the same Gematria. Since there is a concept that Seuda Shelishit has the power to protect one from the future war of Gog uMagog, it is even more beneficial to also include wine with Kiddush during this meal. Rabbi David Messas, however, quotes the Arizal who says that wine represents Divine judgment while Seuda Shelishit symbolizes mercy and thus Kiddush should not be recited during this meal.
The Rashbam (Pesahim 101a) gives two explanations to the concept that Kiddush should be recited in the place of a Seuda (Kiddush Bimkom Seuda). One interpretation is that in order to give importance to Kiddush, it should be accompanied with a meal. The other explanation is that in order to give a meal importance, Kiddush should be recited. It follows, then, that even Seuda Shelishit should include Kiddush. Indeed, the Rambam’s (Shabbat 30:9) opinion is that Kiddush should be recited during Seuda Shelishit. As a compromise, the Arizal states that although a formal Kiddush should not be recited for the aforementioned reason, wine itself should be consumed during the meal. The common custom nowadays is to not recite a formal Kiddush at the beginning of Seuda Shelishit but it is proper to consume wine during the meal.
Summary: Kiddush does not need to be recited for Seuda Shelishit.