Heat oil in a large skillet over medium-high heat.
Add the garlic, ginger, and red pepper flakes. Stir-fry for a few seconds, just until fragrant, then add the cabbage and carrots.
Stir-fry for about 3 minutes until the cabbage begins to wilt, then add the coconut aminos and lime juice.
Cover and cook over high heat for a 2 more minutes until just wilted.
Uncover and stir-fry for another minute, then stir in the cilantro and remove from the heat. The cabbage should be cooked until it's just crisp-tender.