Scoop the avocado into a large bowl and add the beans. Use a fork or a potato masher to mash the white beans and avocado until smooth. Season with the lemon juice, salt, and a few twists of black pepper and mix until combined.
On a clean work surface, place the pieces of toast. Dividing evenly, spread (and pile high!) the avocado mash on the toast. Top with the arugula, cherry tomatoes, and feta. Drizzle each slice with olive oil and balsamic glaze, and finish with a sprinkle of pepper flakes.
