Remove a thin slice from the top and bottom of 2 grapefruits, and discard. Set one of the flat sides on the work surface. From top to bottom, following the curve of the fruit, cut away peel and white pith. Holding fruit over bowl, cut along both sides of each segment (close to the membrane) to release. Reserve segments. Squeeze juice from membrane into a measuring cup. Juice the third grapefruit to total 1 1/2 cups juice.
In a medium non-aluminum saucepan, combine juice, brown sugar, and red pepper flakes. Bring to a boil and cook unti syrupy, about 15 minutes (you should have about 1/4 cup). Remove half of the glaze to bowl and let cool to room temperature.
Add 1 cup of grapefruit segments to the pot (reserve remainder for serving); bring to a boil. Cook, stirring occasionally, until segments have broken down and sauce has thickened, about 12 minutes (you should have about 1/4 cup of relish).
Heat broiler with the rack set 4 inches from the top. Line a rimmed baking sheet with aluminum foil. Place salmon fillets on prepared sheet and season with salt and pepper. Brush salmon with reserved glaze and broil, rotating once during cooking, until opaque throughout, 6 to 7 minutes. Serve salmon with relish and reserved grapefruit segments.