Cómo mostrar filas en paquetes de tres en MySQL

Si está ejecutando MySQL 8.0, considere:

SELECT *
FROM mytable
ORDER BY 
    FLOOR((ROW_NUMBER() OVER(PARTITION BY type ORDER BY timestamp) - 1)/3),
    type, 
    timestamp

Demostración en DB Fiddle :

| id  | type | timestamp |
| --- | ---- | --------- |
| 1   | A    | 101       |
| 2   | A    | 102       |
| 5   | A    | 105       |
| 3   | B    | 103       |
| 4   | B    | 104       |
| 6   | B    | 106       |
| 7   | A    | 107       |
| 8   | A    | 108       |
| 10  | A    | 110       |
| 9   | B    | 109       |
| 11  | B    | 111       |
| 12  | B    | 112       |

En versiones anteriores, puede usar variables para emular ROW_NUMBER() :

SELECT id, type, timestamp
FROM (
    SELECT 
        t.*, 
        @rn := CASE WHEN @type = type THEN @rn + 1 ELSE 1 END rn,
        @type := type
    FROM 
        mytable t
        CROSS JOIN (SELECT @type := NULL, @rn := 1) x
    ORDER BY type, timestamp
) x
ORDER BY 
    FLOOR((rn - 1)/3),
    type, 
    timestamp;

Demostración en DB Fiddle