This is a rather unique question, as most people discuss the title in terms of Gene's separate peace, rather than Finny. I would argue that from the beginning, Finny has a separate peace. He is at ease with everyone around him, and he genuinely seems to be a likable and affable character. He remains friends with Gene throughout the novel, even though Gene plots his downfall and admits to pushing him out of the tree. In fact, after the accident, Finny becomes increasingly dependent on Gene.
It is only when Finny applies for and is rejected from every branch of the military that he needs his "separate peace". Devastated by his inability to join the war effort, Finny seeks any kind of outlet for his sorrow. He finds that through Gene as well. By training Gene for the Olympics, Finny is essentially living vicariously through his friend. That too is shattered by the "trial" set up by Brinker and the other boys. Unfortunately, it is only through his death that Finny truly achieves a separate peace. He is no longer attached to Gene, and their frighteningly codependent relationship can no longer do harm.