Trim ends of brussels sprouts and shred in the bowl of a food processor.
Trim kale, removing thick center stems, and shred.
Heat oil in a large straight-sided saute pan over medium-high heat. When oil shimmers, add shallots and cook until shallots begin to soften and sweat, 1 minute.
Add brussels sprouts, kale, salt, and red-pepper flakes to pan and cook, stirring occasionally, until vegetables are wilted and tender, about 5 minutes. Stir in vinegar, remove from heat, and serve.