Assuming you're planning to use kanamycin for a bacterial infection in the GI tract? - There is at least some data out there suggesting the oral route is the most effective - though oral dosing can be less simple (since the fish is not eating, and there can be toxicity if it decides to eat too much).
From the U of FL: The aminoglycosides, including gentamicin, neomycin, kanamycin, and amikacin, are very effective against gram-negative bacteria infections when administered by injection. Unfortunately, this group has also been shown to cause kidney damage in fish when administered by this technique.
As a group, these antibiotics are not considered effective when used in oral or bath treatments. A couple of exceptions may be kanamycin and neomycin, both of which may be effective against external infections if used in bath treatments. In addition, kanamycin is also believed to be effective when mixed with feed to treat gastrointestinal bacterial infections (Gilmartin, Camp and Lewis 1976).