The Bible tells Christians both to flee sin and to fight/kill sin. How would you explain that these two things are complementary and not contradictory? Thanks!
Speaking only to one part of your question, the only way Scripture would logically be contradictory is if it said both to do X and not do X at the same time and in the same way.
I should probably wait for wiser heads to answer ... but ... Joseph fled when Potiphar's wife tried to seduce him. Job 'made a covenant with his eyes not to look upon a maid. In Galatians 5 Paul talks about the flesh lusting against the Spirit. So I think our response to the struggle with sin depends on the circumstances. Resist the devil and he will flee from you, or ... we do the fleeing if that it the best strategy.
In a sense, asking the question "to flee or to fight" with regard to sin is a tautology. It would be similar to asking, "In salvation, do we turn to Christ or do we turn away from sin?" Well, these two things are really one and the same. In the same way, since sin is something that ought not be done—i.e., it ought to be abstained from—fighting it necessitates fleeing from it, obviously with the element of faith and trust in Christ and in the Spirit's work of sanctification.