MySQL-Query - Can´t get the right result

I would like to get the latest msg from each msgconv where a specific user is involved

If you are running MySQL 8.0, you can use ROW_NUMBER() to identify the records to display:

SELECT *
FROM (
    SELECT 
        m.*,
        ROW_NUMBER() OVER(PARTITION BY msgconv ORDER BY timestamp DESC) rn
    FROM msg m
    WHERE 
           ( msgfrom = 69 AND msgdel_sender = 0 )
        OR ( msgto = 69 AND msgdel_receiver = 0 )
) x

In earlier versions, you can use a NOT EXISTS condition with a correlated subquery:

SELECT *
FROM msg m
WHERE 
    ( 
           ( msgfrom = 69 AND msgdel_sender = 0 )
        OR ( msgto = 69 AND msgdel_receiver = 0 )
    )
    AND NOT EXISTS (
        SELECT 1
        FROM msg m1
        WHERE 
            (
                   ( m1.msgfrom = 69 AND m1.msgdel_sender = 0 )
                OR ( m1.msgto = 69 AND m1.msgdel_receiver = 0 )
            )
            AND m1.msgconv = m.msgconv 
            AND m1.timestamp > m.timestamp
    )

The query starts by selecting all records that belong to the relevant user. Then, the NOT EXISTS condition filters out every record but the latest in each group of record having the same msgconv.