Problema con la consulta de MySQL usando AVG()

Si realmente se actualizan todos los días, utilice la aritmética de fechas:

SELECT bline_id, AVG(flow) as flowavg
FROM blf
WHERE bline_id BETWEEN 1 AND 30 and
      date >= date_sub(now(), interval 10 day)
GROUP BY bline_id
ORDER BY bline_id ASC

De lo contrario, debe colocar un contador, lo que puede hacer con una subconsulta correlacionada:

SELECT bline_id, AVG(flow) as flowavg
FROM (select blf.*,
             (select COUNT(*) from blf blf2 where blf2.bline_id = blf.bline_id and blf2.date >= blf.date
             ) seqnum
      from blf
     ) blf
WHERE bline_id BETWEEN 1 AND 30 and
      seqnum <= 10
GROUP BY bline_id
ORDER BY bline_id ASC