The business code is not on K-1s but is on the 1065/1120S main form. You'll have to contact the K-1 provider for that information.
The list of business codes for Schedule C is at the end of the instructions: https://www.irs.gov/pub/irs-pdf/i1040sc.pdf
Or if you have a good idea of what the K-1 business is then you may be able to look it up yourself: https://www.naics.com/search/
