I looked at the clinical trial in your link. They are testing vitamin D3 (calcitriol) as a supplement to chemo. Vitamin D3 is readily available in any pharmacy. So to answer your question.... yes, you can easily do this at home if you wish. As always, it's a good idea to check with your oncologist before you add a new supplement.
Keep in mind, our bodies produce TONS of vitamin D3 when exposed to sunshine. As a southerner, you probably get more than enough vitamin D3 when you go outside in the sunshine.
On the other hand, I heard that sunshine exposure is not recommended during chemo. Do you take special precautions to hide from the sun?