I've been doing the swap breeding method for the last few months, and had no success. Frustrated, I looked into the RNG behind it all and discovered something while reading this:
http://tellu.wpblog.jp/rng-abuse/7thgen-rng-abuse/guide-for-breeding-abuse-on-sunmoon/Assuming I'm understanding this correctly, rejecting an egg advances you 1 single frame, whereas accepting an egg advances you many more frames (20-40), potentially skipping over eggs that could be shiny.
For simplicity sake, say you just started and are on Frame 1. Your shiny egg is on Frame 29. Accepting an egg advances you 27 frames. So then you end up on Frame 28, but by accepting the next egg, you skip over the frame you needed to hit to get the shiny egg.
What should be done is reject the first egg, then collect the next egg generated, and wa-la, you hit the 29th frame that will give you the shiny egg.
As the swap method currently states in the tutorial at the bottom of pic-related, your supposed to hatch 30, and if no shiny, save the game, and collect another batch.
However, what should be suggested for Step 6 is this:
after hatching 30 eggs, if no shiny, soft reset the game. Then, when the first egg of that batch of 30 is generated, REJECT it, save right after (so there's enough time to swap should the next egg actually be shiny), and collect another 30 eggs to hit a different set of frames than before.
Please let me know if I've misunderstood anything above. I think I've got it figured out, but I wanted to ask around first before spreading any misinformation.
I'm in the midst of testing out this theory for myself. I did start rejecting eggs a few days ago, and finally got my shiny Magikarp, and was able to swap it with an HA Starly.
If others are willing to join me by doing some testing of their own, that would be greatly appreciated.