Using a sharp knife, chop the salmon until it's in small chunky pieces. Alternately, you can also add it to a food processor and pulse it a few times until chopped through. Transfer to a large bowl and add in the bread crumbs, mayo, lemon juice, salt, pepper, red pepper flakes, and herbs. Give it a mix until just combined. Divide into four equal portions and then shape each into a large 1/2-inch patty. Place on a baking sheet lined with parchment paper and chill for at least 30 minutes or up to 1 hour.
Set a large non-stick skillet over medium-high heat with half of the oil. Once hot, place two of the patties in and cook until crispy and browned, with an internal temperature of 125° to 130°, about 4 to 5 minutes per side. Transfer to a wire rack set over a baking sheet. Add in the remaining oil to the skillet and cook the remaining two patties in the same way.
To assemble the burgers, spread each toasted bagel half with cream cheese. Place a salmon burger on top of each bottom half of the bagels. Top with tomato slices, red onion, cucumber, capers and fresh dill. Place the top half of the bagel on and serve immediately. Enjoy!