Make dressing/marinade. Whisk together olive oil, red pepper flakes, lime juice, garlic and cumin until emulsified.
Place chicken breasts in a large resealable plastic bag. Pour about half of the lime dressing over the chicken, close bag and toss chicken to coat.
Marinate 15 minutes. Meanwhile, heat 2 tablespoons vegetable oil in a medium skillet over medium heat. Cut tortillas in half, then slice the halves into ½”-thick strips. When the oil is shimmering and very hot, add the strips to the oil. Fry until crispy, about 2 minutes per side. Drain on paper towels and season immediately with salt.
In a separate skillet, heat remaining vegetable oil over medium-high heat. Add chicken and cook for 6-8 minutes per side, until the chicken is cooked through. Let rest for 10 minutes before slicing.
Assemble salad. Toss remaining ingredients in a large serving bowl. Top with cooked chicken and crispy tortilla strips then toss with dressing.
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