The Gemara (Pesachim 100b) writes that the Chazan recites Kiddush in Shul on Friday night for the guests who would stay in the Shul. As nowadays, guests don’t typically eat their Shabbos meals in the Shul, the Tur (OC 269) writes that this custom no longer applies. Rambam (Shut Harambam 37) however, writes that although the reasoning may no longer apply, we shouldn’t abandon a takana of the Rabbis. The Beis Yosef (OC 269) quotes a few Rishonim who defend the practice, yet paskens like the Tur that one shouldn’t. The Tashbetz (quoted by his sons in Shut Yachin Uboaz 1:118) held that one shouldn’t even answer Amen to Kiddush in Shul as there is a safek of a bracha levatala.
Nonetheless, the Mishna Berura (269:5) writes that the accepted minhag is for the Chazan to recite it. R’ Ovadia Yosef (Yalkut Yosef 269:2) writes that a Shul that doesn’t usually say it should change their custom if there is anyone in Shul that won’t otherwise say Kiddush. The Shulchan Aruch writes that as he is not going to eat immediately after (Kiddush B’makom Seuda), the Chazan should give the wine to a child. If there is no child present, the Chazan should drink at least a Revi’is, say a Bracha Achrona, and have intent to fulfill the mitzvah of Kiddush. This does not prevent him from later making Kiddush again at home (Mishna Berura 269:1, Yabia Omer 1:15).The pre-war minhag in Finland was always to recite Kiddush, though as wine was scarce during the war, they stopped this practice. The Chief Rabbi asked R’ Yechiel Yaakov Weinberg whether he should reinstate this minhag. He was reluctant to do so based on the Beis Yosef. R’ Weinberg replied (Seridei Aish 2:157) that the Shul should begin doing so again as it adds grace and beauty of holiness to the start of Shabbos. Additionally, it may inspire others who wouldn’t otherwise make Kiddush, to do so when they return home.