The dose I have is a 5mg/kg loading dose for the first injection followed by 2.5 mg/kg every 72 hours. Another tortoise dose is 5 mg/kg every 24 hours (which is obviously much higher, but I would be a little concerned about such a whooping dose as 10 mg/kg all at once even if only every 72 hours. I would rather give more frequently at a lower dose. But, I have not seen your tortoise and I am not a veterinarian!). Both of these doses are from Carpenter, et al "The Exotic Animal Formulary". It depends on the severity of the infection. I would defer to your veterinarian, as they have (hopefully) diagnosed the problem with xrays and /or bloodwork.
I would always rec. increasing hydration during the use of any medications in reptiles, but especially aminoglycosides like Amikacin. It has the potential to be nephrotoxic and you will want to keep good perfusion to the kidneys to protect them. Daily soak should suffice, I would imagine if your tortoise was in such bad shape that it needed IV or IC fliuds your veterinarian would have either hospitalized your tortoise or adminstered them. Hope this helps.
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Stacey