The sentence is talking about seven flavors. Flavors is a plural noun. The verb should also be plural. The verb is in the contraction There's which means There is. It should be There are. This is the wrong part of the sentence.
The error in the sentence "There's now seven new flavors" is THERE'S.
"There is" refers to nouns in their singular form since "is" goes with singular subjects and objects. In this particular case, the correct option should be "there are" in order to collocate with the "seven flavors" (plural form of the noun flavor) mentioned in the sentence. "ARE" is the form of the verb to be that refers to the plural form of the words.
