It is not dangerous, but it is not necessary.
Sourdough starter is not going to ruin it, but it is not going to be REAL kimchi. Kimchi is really easy to make plus it tastes better when naturally fermented. Some people even prefer to ferment it in the fridge. It is going to take longer, but it's going to taste differently.
The is nothing unnatural about the SS, but SS is not natural for fermentation of kimchi. It is not used traditionally. It also might alter the kind of yeast and bacteria that are present in kimchi. The microorganisms present in naturally fermented kimchi are: Bacillus mycoides, B. pseudomycoides, B. subtilis, Lactobacillus brevis, Lb. curvatus, Lb. parabrevis, Lb. pentosus, Lb. plantarum, Lb. sakei, Lb. spicheri, Lactococcus carnosum, Lc. gelidum, Lc. lactis, Leuconostoc carnosum, Ln. citreum, Ln. gasicomitatum, Ln. gelidum, Ln. holzapfelii, Ln. inhae, Ln. kimchii, Lactobacillus kimchii, Ln. lactis, Ln. mesenteroides, Serratia marcescens., Weissella cibaria, W. confusa, W. kandleri, W. koreensis, and W. soli. The bacteria and yeast present in SS are somewhat different.
If you are going to add some sourdough starter, it will still come out well, but it's not going to be authentic. My question is: do you want to make REAL kimchi (김치) or do you want to make your own version of kimchi?
As an avid supporter of Korean cuisine, I want to take it one step further: James Oliver's recipe doesn't sound very Korean (sorry). He omits Asian pears and adds daikon which is predominantly used in radish kimchi (깍두기).
From my personal experience, kimchi tastes best when it is naturally fermented, no starter needed.
I also recommend an authentic Korean recipe which is surprisingly easy to make, here it is:
The only thing that I personally do differently, I don't add sugar at all, just more Asian pears. It still comes out nice.