I tend to read only on AO3 bc my phone dislikes KS archives. I would say that at least 90% of the AOS K/S fics are bottom!kirk (and hurt!kirk is one of the most common themes). I would say go to the AOS tag and scroll through, sorting by word count, and you'll find A LOT. Bottom!hurt!jim is my absolute favorite, so feel free to stroll through my bookmarks, as well, for ones you might like. I sorted by pairing: K/S bookmarks (http://archiveofourown.org/bookmarks?utf8=%E2%9C%93&bookmark_search%5Bsort_column%5D=created_at&bookmark_search%5Bcategory_ids%5D%5B%5D=23&bookmark_search%5Bfandom_ids%5D%5B%5D=601802&bookmark_search%5Brelationship_ids%5D%5B%5D=9835&bookmark_search%5Bother_tag_names%5D=&bookmark_search%5Bquery%5D=&bookmark_search%5Brec%5D=0&bookmark_search%5Bwith_notes%5D=0&commit=Sort+and+Filter&user_id=scifishipper)

You could also do a general search on AO3 for hurt!jim. I don't think you'll find that many tags for bottom!jim, because it is SO SUPER COMMON. This is a search for Kirk/Spock hurt/comfort. (http://archiveofourown.org/works?utf8=%E2%9C%93&commit=Sort+and+Filter&work_search%5Bsort_column%5D=word_count&work_search%5Bfreeform_ids%5D%5B%5D=2379&work_search%5Bother_tag_names%5D=&work_search%5Bquery%5D=&work_search%5Blanguage_id%5D=&work_search%5Bcomplete%5D=0&tag_id=James+T*d*+Kirk*s*Spock)

I hope this helps. Good luck!