Mix the cream cheese, sour cream, garlic powder, lemon zest, salt, and dill in a bowl until smooth and creamy.
Place one flatbread on a board, spread half of the mixture evenly in a square shape, and layer half the smoked salmon slices on top.
Spread a thin layer of butter on the second flatbread, place it butter side down over the salmon, then spread the remaining mixture on top in the same square shape and layer the rest of the salmon.
Spread a thin layer of butter on the third flatbread and place it butter side down on top to finish the stack, then press lightly with a cutting board or flat object to smooth and compress everything.
Cover the stack tightly with cling wrap, refrigerate for at least 4 hours or up to 48 hours so the filling sets, then use a serrated knife to trim the edges, cut the stack into 6 or 7 strips, slice each strip into small squares, and serve with toothpicks, lemon wedges, and extra dill.