Why is the sentence 'She loves flowers' is transitive?

It is a transitive sentence because the verb to love is transitive.

Transitive verbs are those which demand a direct object after them. Here, the verb is to love, and its direct object are flowers. You can easily see if a verb is transitive by asking the question - What?

What does she love? - Flowers.

Since we have an answer, it means that the verb, and the entire sentence, are transitive.