Question:
What is a brother's chiyuv to say Kaddish for a sister who has no husband or children?
Answer:
If it is hard for him, he doesn't have a chiyuv, however it would be very helpful for her neshoma to say one kaddish at each tefillah until the shloshim. In general, it isn't only the kaddish, and any other mitzva that is done in her merit will be helpful for her neshoma.
Best wishes