@micmc Doesn't work unfortunately:
mysql> SET slow_query_log = 'ON';
ERROR 1229 (HY000): Variable 'slow_query_log' is a GLOBAL variable and should be set with SET GLOBAL
...meaning it has to be set as a global variable. Logging a single database isn't possible apparently. The app level user doesn't have access to set global variables:
mysql> SET GLOBAL slow_query_log = 'ON';
ERROR 1227 (42000): Access denied; you need (at least one of) the SUPER or SYSTEM_VARIABLES_ADMIN privilege(s) for this operation