The Shulhan Aruch (O.H. 272:10) rules that the blessing of Kiddush over wine exempts other beverages that are drunk during the meal from their own blessing. Furthermore, one does not need to recite an after-blessing for wine as it is exempted by Birkat Hamazon. Thus, if one wishes to drink cola, fo example, during the Shabbat meal, one would not have to recite “Shehakol”, and one would also not need to recite “Al Hegefen” as an after-blessing for the wine of Kiddush.
The Biur Halacha (O.H. 174) cites an opinion that Kiddush only exempts other beverages from their own blessing when one drink at least a cheekful of the wine or grape juice of Kiddush in one shot. If one simply sips a little of the Kiddush, it would not exempt other beverages, according to this opinion. Nevertheless, Rabbi Ben Zion Abba Shaul (Or Lezion, vol. II, ch. 20, § 9) says that as long as one drinks even a little amount of wine, one would not recite a separate blessing on other beverages during the meal.
Interestingly, he Ben Ish Hai (Rav Pe’alim, vol. II, Orah Haim, §47) says that the Arizal received a Divine teaching that if one drank a Revi’it or more in one shot of a beverage during the meal, one would need to recite the after-blessing of “Bore Nefashot” and could not rely on Birkat Hamazon. The Ben Ish Hai (Shana I, Parashat Naso, §2), the Kaf Hahaim (K.H., O.H., 272:63) and Rabbi Ben Zion Abba Shaul (ibid., ch. 12, § 6) all concur.
Notwithstanding, Rabbi Shalom Messas (Tevuot Shamesh, Orah Haim, § 62) writes that there was never such a custom to make an after-blessing for a drink during the meal, and that Bikat Hamazon exempts all beverages that are consumed during the meal, regardless of the quantity. This, too, is the opinion of Rabbi Ovadia Yosef (Halichot Olam, vol. II, pg. 27), who says that an after-blessing is never said on beverages during the meal.
Summary: Kiddush exempts all beverages that are drunk during a meal from their own blessing. Birkat Hamazon exempts all beverages during the meal from an after-blessing, regardless of quantity.