Why the sentence 'She loves flowers' not a transitive sentence?

It is a transitive sentence. The verb to love is a transitive verb because it demands a direct object after it. What does she love? Flowers. So, this is a transitive sentence. If your test says it is not, then the test is wrong.

However, you could argue that the verb to love is not an action verb and that it would be the reason why it is intransitive, however, grammarians generally disagree on that.