Scieszka. The Book That Jack Wrote

The Book That Jack Wrote is a children's book by Jon Scieszka, with art by Daniel Adel, published in YEAR. It is available at the Internet Archive.

Here is a YouTube read-along:

The text of this book plays with the traditional "Jack" story by starting out with the initial cow-dog-cat-rat series, but then things become more whimsical, inspired by other nursery rhymes and literary figures... and then, a man in a "tattered" coat shows up (echoing the man "tattered and torn" from the traditional Jack... and that man IS Jack. You can see how it all fits together as the chain concludes; note the rhyming couplets:

This is the Book that Jack wrote,
That squashed the Man in the tattered coat,
That stomped the Bug, 

That frayed the rug,

That tripped the Hatter in the hall,

That knocked the Egg falling off the wall,

That startled the Pieman at the fair,

That flung the Pie flying through the air,

That beaned the Baby humming the tune,

That tossed the Cow sailing over the moon,

That spooked the Dog,

That chased the Cat,

That ate the Rat,

That fell in the Picture...

That lay in the book that Jack wrote.

The artwork is whimsical in a way that suits the story very nicely: