。
She says she likes flowers.
Literal
She [topic-は] flower [subject-が] like is [quotative-と] is-saying.
Reporting what someone says uses the embedded clause + quotative と + 言う pattern: ~と言う = 'say that ~.' Add ~ている for the resulting state and you get 言っている — 'is saying' or 'has been saying / has said.' For repeated utterances or reports of ongoing claims, the ~ている form is the natural choice; bare 言った would mean 'said (one specific time).' Inside the embedded clause the original speaker's だ is preserved unchanged — Japanese keeps direct and indirect quotation more similar than English does.