Import/export by sector/country data source
I believe that the UN Comtrade database is the main data source for this kind of query with substantial country coverage.  It's broken down by HS code.

It has its issues.  Reporting is based on national authorities, so you should usually expect data on imports to be more accurate than exports because of the tax implications (so Uganda's imports from Kenya are likely to be more accurate than Kenya's exports to Uganda).