This sentence sounds wrong to me: The Singing Mermaid

[Strippe]

I feel that they didn’t need to say ‘he said’ twice. When I’m reading this aloud to my dd it trips up the flow.

Yup, maybe it flows better in an accent other than mine.

Well yeah because the second 'said' is meant to rhyme with 'bed.'

Its rhyming couplets.

It’s fine? 3 beats per line. Consistent iambic feet.
He SAID, I can MAKE you FAmous
I can MAKE you RICH, he SAID
You shall SWIM in a POOL of MARble
And SLEEP on a FINE feather BED

No it isn’t. It’s an ABCB rhyme scheme.

It’s clunkily written. I used to stumble over that line too. Anaphora works much better with ‘He said’ beginning both lines but ‘rich’ doesn’t rhyme with ‘bed’ so …

The rest of the book doesn’t flow like that though. Even if you watch it being read on YouTube it sounds off.

In the second stanza the third line has 4 beats but I think it still works nicely. If you pause for a beat at the end of every line except that one it gives a nice overall rhythm.

Well, it's a poem. Not a brilliant one, but repetition for the sake of rhythm and rhyme, and sometimes for its own sake, is pretty standard in a poem.

Read by who? Maybe they just did a bad job of it?