Not sure what they are getting at and some of the info is flawed. There is absolutely no evidence that suggests garlic boosts any immunity.
Strontium has been implicated in a number of things and isn't necessary for calcification or health, however, Reef Crystals has more of it than Instant Ocean (pers. comm. with customer rep, though years ago). There is nothing wrong with using Instant Ocean.
As far as the potential risk of adding the kanamycin to the food and consequently into the tank, there is potential risk, as with anything. The best thing I can tell you to do is to do what I mentioned above, maybe invest in getting a skimmer (which would be very effective at removing it), and have water ready for water changes. Adding any sort of antibiotic is my last choice (and certainly to a reef tank) but this is the safest way to do it short of having a hospital system and you won't be adding it directly to the water at full dose. The food method is more of an "at your own risk," though I think when done properly and carefully, you can minimize a lot. Seachem has another product called "Focus" that is supposed to be a binder. I would highly recommend you try this in conjunction with everything else if you still want to try this. Beyond that, a bath approach for skin issues would arguably be slightly more effective than orally, but oral administration works for all but the most stubborn infections. Again, a hospital tank is always the best and safest approach, but I think you already knew that adding it even just to feed isn't without risks.
