Stir together the lime juice, apple cider vinegar, sugar, and kosher salt in a large jar or bowl until the sugar and salt dissolve completely, about one minute of stirring.

Add the sliced cucumbers, jalapeño, and red onion to the brine. Toss everything so the cucumbers are evenly coated. Seal the jar or cover the bowl and refrigerate for at least two hours. The cucumbers will soften slightly and turn a little translucent at the edges, which means the brine has done its job.

When you are ready to serve, cut the avocados in half, remove the pits, and use a spoon to scoop out the flesh. Cut into chunks about three quarters of an inch wide. Keeping them on the larger side means they will hold their shape when folded in rather than breaking down into a paste.

Use a slotted spoon to lift the pickled cucumbers out of the brine and into a serving bowl. Leave most of the liquid behind so the salad is not soupy, but keep a few tablespoons of the brine in the bowl for flavor.

Add the avocado chunks and cilantro to the cucumber mixture. Fold everything together gently with a spoon or rubber spatula, turning just two or three times so the avocado stays in distinct pieces.

Scatter the red pepper flakes over the top and taste for salt. Add a small pinch more if needed. Serve right away at the table.