Learn English – When a sentence uses a parenthetical plural, should the rest of the sentence treat it as singular or plural

Singular and plural are both correct.

The singular form is also used because "two and two" is an arithmetic formula. The verb agreement in that case is with the formula as a single entity.

• Two and two makes four.

• Two plus two is four.

• Four times four divided by two is
  eight.

In your example in particular, Google indicates that the plural form occurs more often:

"two plus two make four" = 353K results
"two plus two makes four" = 77K results

And while Google hit counts are notoriously, the result is supported by Google Ngrams.

One of the problems is flags.

This is grammatical because the subject of the verb is is the singular pronoun one. Trim away the prepositional phrase and the predicate, and you get:

One... is...

... which is obviously correct.

One is very frequently used with a prepositional complement containing a plural noun, such as of the problems. This does not change the grammatical number of the subject.

One of the boys is sick.

One of the trees is falling over.

One of the candidates will win.

The only further wrinkle in this sentence is the fact that the predicate nominative flags is also plural. This, too, does not change the number of the subject, and it fact joining a singular subject with a plural predicate nominative is very common in English.

Open-source is many different developers working together freely.

A woman is not just her breasts.

So there really isn't anything ungrammatical about the original form of the sentence. Some people may find it infelicitous, and it could probably be reworded for clarity or style, but it isn't violating any of the rules of English grammar.