Hi Astrid. I'm in BC. There's likely no clear policy about this, certainly none that I'm aware of, despite years of homeschooling and communicating with other homeschoolers in this province. Obviously if your child was enrolled in school and was travelling out of province for more than 30 or 60 days or whatever, there would be concerns about mastery of the school curriculum and suggestions that he be registered in the other province so he wouldn't miss too much. But that wouldn't apply to homeschooling. Your school of registration will be happy for the funding your son garners for them, and you should just be honest that "we travel frequently, but our permanent home address is _____ ," and don't be any more specific about it than that. In Alberta or Ontario or wherever you're travelling to, if you're questioned, you should just say "he's enrolled in an electronically mediated independent school for distance learning, based in BC, our place of permanent residence". Kindergarten isn't even compulsory in any province except, I believe, NB, so you wouldn't even need that exaplanation next year.
I know sevearal families who have moved from province to province whilst homeschooling, and they have all waited until the following fall to change their registration/notification over to the new province. This sort of falls along the same lines.
Homeschooling is regulated in a pretty trusting way in most provinces. Although some provinces are a little more intrusive than others in their regulation, no Ministries of Education north of the 49th really seem to perceive homeschooling as a threat that needs watchdog control. Reasonable approaches generally prevail. I wouldn't sweat it. Just imagine you're taking frequent weeklong trips... week after week.

Miranda
in the Kootenays, where it's currently raining both rain and ash from forest fires