Problema com consulta MySQL usando AVG()

Se eles forem realmente atualizados todos os dias, use a aritmética de data:

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

Caso contrário, você deve colocar um contador, o que pode ser feito com uma 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