The optimization process and recommendations:

1. Avoid Correlated Subqueries (query line: 4): A correlated subquery is a subquery that contains a reference (column: records_round_id) to a table that also appears in the outer query. Usually correlated queries can be rewritten with a join clause, which is the best practice. The database optimizer handles joins much better than correlated subqueries. Therefore, rephrasing the query with a join will allow the optimizer to use the most efficient execution plan for the query.
2. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
3. Sort and Limit Before Joining (modified query below): In cases where the joins aren't filtering any rows, it's possible to sort and limit the amount of rows using a subquery in the FROM clause, before applying the joins to all other tables.

Optimal indexes for this query:

ALTER TABLE `records` ADD INDEX `records_idx_player_id_id` (`player_id`,`id`);
ALTER TABLE `records` ADD INDEX `records_idx_id` (`id`);

The optimized query:

SELECT
        SUM(records_kills) / SUM(t1.duration) * 60 * 60 kills_hour_last_10 
    FROM
        (SELECT
            records_kills,
            rounds.duration 
        FROM
            (SELECT
                records.kills AS records_kills,
                records.round_id AS records_round_id 
            FROM
                records 
            WHERE
                records.player_id = 1 
            ORDER BY
                records.id DESC LIMIT 10) AS records 
        JOIN
            rounds 
                ON rounds.id = records.records_round_id 
        WHERE
            1 = 1 LIMIT 10
        ) t1