Heat olive oil in a large pan over medium heat. Add onion and cook until beginning to caramelize, about 10 minutes. Add tuna with oil, capers, and red pepper flakes; heat through.

Meanwhile, bring a large pot of lightly salted water to a boil. Cook spaghetti in the boiling water for 1 minute less than the package suggests, about 10 minutes. Stir occasionally to prevent sticking. Drain, reserving 1/2 cup of the starchy pasta water.

Add cooked pasta to the pan with tuna and mix to combine. Add some of the pasta water and toss lightly until pasta is tender yet firm to the bite, 1 to 2 more minutes. Sprinkle with chopped parsley and serve immediately.