For the goat cheese: Preheat the oven to 400 degrees F. Line a small baking sheet with parchment and set aside.
Stir together the goat cheese, basil, lemon and salt with a rubber spatula in a medium bowl.
Lay one sheet of phyllo flat in front of you. Brush it gently with some of the oil. Lay another piece of phyllo on top and brush gently with more oil. Continue two more times to have 4 sheets of phyllo. Cut the dough into 5 strips. Scoop a tablespoon of the goat cheese mixture onto one end of a strips. Bring a corner up and over the cheese to line up the bottom edge with the right edge of the phyllo forming a triangle. Continue to do this, folding the phyllo like flag, until you have a little triangle goat cheese package. Continue with the remaining strips and repeat the process with remaining sheets of phyllo. Place the triangles on the prepared pan and brush the tops with more oil. Sprinkle the tops with a pinch of salt. Bake until golden brown and crispy, about 12 minutes.
For the salad: Whisk together the oil and lemon juice in a large bowl. Season with the salt. Add the greens and toss gently to coat. Sprinkle with the flower petals and toss gently to coat. Pile the salad on a platter and place the goat cheese packs around the salad.