Mysql FLUSH LOGS in live server with replication
FLUSH LOGS; is safe to do anytime.  It will rotate the replication logs; this is harmless; replication knows how to move on to the next log.  The binlog is automatically rotated when it exceeds max_binlog_size.

Before 5.6, FLUSH LOGS did not rotate the slowlog.  See http://dev.mysql.com/doc/refman/5.6/en/flush.html or the page for your version.

I have never done reset master; I would not include it.  I use expire_logs_days for automatically purging binlogs.  (If a slave has been offline for that many days and I don't notice it, I deserve the hassle.)

I prefer log_queries_not_using_indexes = OFF; otherwise it clutters the slowlog.  (A tiny table without an index is often not-a-real-problem.)