The one that pops up immediately to me is R&H's Cinderella! And Green Finch and Linnet Bird from Sweeney Todd Don't remember any other flute parts in particular but Seussical has some pretty different orchestrations (symphonic orchestra but with a twist). Other favorites orchestrations of mine are Anything Goes, Porgy and Bess, and Ragtime. I'll add more when I can think of them! Sorry, I'm an oboe player so most of my favorites are somewhat oboe heavy (not always) but that also means that flute is right there in the music as well
Very prominent in the "Put on a Happy Face" (Bye Bye Birdie) orchestrations by Robert Ginzler. So prominent that they have become known in orchestration terms as "Ginzler Flutes". Jonathan Tunick, a mentor of Robert Ginzler, seems to have orchestrated an homage to Ginzler with Ginzler Flutes in "What Around for the Girls Upstais" (Follies).
Like seahag said "Ragtime" does come to mind especially in Back to Before. Also, "Fiddler" uses a flute very often. It's most prominent in the entire wedding scene.
As a former flutist (back in elementary and high school days) I always loved the use of it in the "Il Muto Ballet" in Phantom, and the solo in Sunset Boulevard that transitions us from Norma shooting Joe into the next morning and Norma's entrance in her Salome costume (though of the two I preferred the use of the "Surrender" melody on the London recording over the title song melody on the American recording)