In a small bowl, combine lime juice, oil, oregano, and chili powder; season with salt and pepper.
Place chicken in a resealable bag and pour in marinade. Let chicken marinate at room temperature at least 30 minutes or refrigerate up to 2 hours.
In a medium bowl, whisk oil, vinegar, jam, and honey; season with salt. Refrigerate until ready to use.
Make Ahead: Dressing can be made 1 week ahead. Cover and keep refrigerated.
In a medium skillet over medium heat, heat oil. Remove chicken from marinade; discard marinade. Cook chicken, turning occasionally, until golden brown and an instant-read thermometer inserted into thickest part registers 165°, 8 to 10 minutes per side. Transfer to a cutting board. Let rest 5 minutes before slicing.
Divide spinach between bowls. Top with chicken, cucumber, onion, avocado, blackberries, feta, and walnuts. Add dressing and toss to combine.
