Pat the octopus tentacles dry and toss them with 2 tablespoons of the olive oil, salt, and black pepper.
Heat a grill or large cast-iron skillet over high heat until very hot. Place the tentacles on the surface and cook for 3 to 4 minutes per side until charred in spots and heated through.
While the octopus cooks, combine the sliced fennel, blood orange segments, and chopped parsley in a large bowl.
Whisk the remaining olive oil with the lemon juice and red pepper flakes, then pour over the fennel mixture and toss to coat.
Slice the charred octopus into manageable pieces and arrange on top of the salad. Serve right away.