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Answer: While any amount of food requires a beracha rishona (=br) before it, there is a ba only after eating a k’zayit (Shulchan Aruch, Orach Chayim 210:1). If one eats small amounts of foods with different berachot acharonot that combine to form a k’zayit, he recites the "lower beracha" (usually, Borei Nefashot) (Magen Avraham 210:1).
The question is how to view a single food made up of different ingredients. Regarding br, when a food significantly contains (not as filler) wheat or other flour of the "five minim" (=5mn) along with even a majority of foods with other berachot, one recites only Mezonot (or Hamotzi), which covers even the non-Mezonot ingredients (Shulchan Aruch, OC 208:2).
Regarding ba, in one place, the Shulchan Aruch (ibid.) says that the ba for such a food is Al Hamichya even if the flour is clearly a minority. In another place (ibid. 9), he writes that if there is not a k’zayit of flour within a pras (eight k’zeitim) of food, one recites only Al Hamichya on bread made from it, and if cooked, only Borei Nefashot rather than Al Hamichya. So, we see that the ba can be reduced due to the presence of a predominance of other ingredients. How much it is affected is disputed, as the Gra (ad loc.) says that without a k’zayit within a pras worth the ba is always Borei Nefashot. The Mishna Berura (ad loc. 47) contends that in order to make the higher beracha, the Shulchan Aruch requires not only a one eighth concentration but that one needs to eat a k’zayit worth of the 5mn flour. Conceptually, this means that a minority of flour is central enough to a complex food to control its overall identity and justify a "higher-level" ba, but the other foods are not subsumed enough to counts towards the ba of the 5mn flour.
There is significant machloket to what extent to limit the power of flour regarding ba. The Magen Avraham (208:15) says that the latter, more limiting Shulchan Aruch refers to the mixing of multiple types of grain but that other non-Mezonot ingredients team up with flour to reach the necessary k’zayit. The Chayei Adam (I, 50:21) is among those with misgivings over the Magen Avraham’s distinction. The Mishna Berura (208:48), in noting that the common practice is to recite Al Hamichya after a k’zayit of a piece of cake, even though it has less than a k’zayit of flour, gives the following explanation. Since "spices" (e.g., sugar, oil) are there to improve the prominent flour base, they are counted toward the k’zayit. Another idea is that the minimum amount of liquid needed to turn the flour into dough (but not the extra that makes it loose batter) counts toward the k’zayit (V’zot Haberacha, p. 236). The Chazon Ish (OC 26:8) similarly distinguishes between ingredients that are kneaded along with the flour, which count toward the k’zayit, and ingredients that are added after the kneading (e.g., the chocolate in rugelach). In the other direction, in cases where ingredients form a very distinct filling, e.g., in apple pie, it is accepted that it does not count toward the k’zayit (V’zot Haberacha, p. 47).
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