In a small bowl, whisk together the olive oil, red wine vinegar, lemon juice, oregano, salt, black pepper, and red pepper flakes until well combined. The acidity from the vinegar and lemon juice will help balance the richness of the oil and create a bright dressing that coats all the ingredients evenly.
While the vinaigrette sits, prepare your mise en place: halve the grape tomatoes lengthwise, dice the cucumber into bite-sized pieces, thinly slice the red onion (I like to slice it paper-thin so it doesn't overpower the delicate tuna), and roughly chop the parsley. Having everything prepped and ready will make assembly quick and ensure even distribution of flavors.
Add the cucumber, tomatoes, onion, and parsley to a large bowl. Pour the vinaigrette from Step 1 over the vegetables and toss gently to combine, making sure everything is evenly coated with the dressing. Let this sit for a few minutes so the vegetables can absorb the flavors.
Open and drain the canned tuna and cannellini beans, rinsing the beans under cold water to remove excess sodium. Gently fold the tuna, beans, and crumbled feta cheese into the vegetable mixture, being careful not to break up the tuna too much—you want some nice flakes rather than shredded pieces. I find that folding rather than stirring keeps the texture more appealing and prevents the salad from becoming mushy.