Look at Minion Ornaments, Linotype Decoration Pi One, Type Embellishments One for starters. You can probably find them all at fontshop.com or myfonts.com. I don’t feel like searching for the links.

Calligraphic ornaments can be found in font form, digitized clip-art, etc.

It also depends on what period or style of calligraphic flourish or ornament you are looking for.

Try looking at Ornament fonts available at Typoasis.

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Yes, I’m old, but I can still flourish!

There are some nice ornaments in the Illustrator CS Symbol Library, Decorative Elements.

Not free but Dalliance from Emigre has some wonderful swash elements