The sentence is:
I just need some help understanding how this sentence is structured and what 'kita ki ga suru' indicates over here?
The separation is incorrect. It should be: 分かってきた / きがする
分かってきた here it means “finally understand”.
きがする (usually written as 気がする) means “I think...” in this context.
So the sentence means “I think I finally understand a little bit, but I may have got it wrong though.”