Heat oil inside Instant Pot on Sauté mode. Add onion and cook until soft, about 3 minutes. Add garlic, cumin, chipotle chili powder, and salt. Cook for 1 minute. Stir in broth, chicken, and beans. Press ingredients down into broth. Close and lock pressure cooker lid. Cook on HIGH pressure for 8 minutes.
Manually release pressure and remove chicken to cutting board. Shred or chop chicken. Stir chicken, kale, cilantro, and lime juice into soup. Let the kale wilt slightly, about 5 minutes, and serve.