4 species have Quick Feet as a hidden ability, 5 as a normal one

Effect, in PokéAPI's words

“Increases Speed to 1.5× with a major status ailment.”

As a hidden ability

Species	Slot	Note
Jolteon	Hidden	Since Generation V
Zigzagoon	Hidden	Since Generation V
Linoone	Hidden	Since Generation V
Shroomish	Hidden	Since Generation V

As a normal ability

Species	Slot	Note
Granbull	Normal
Teddiursa	Normal
Ursaring	Normal
Poochyena	Normal
Mightyena	Normal

Elsewhere in PokéAPI

2 more holders without a page here

Alternate forms and other species that PokéAPI lists with Quick Feet.

Zigzagoon Galar (hidden), Linoone Galar (hidden)