Is it internal/unpublished sequence or from one of the existing genomes? If it is a sequenced genome, this is possible from either BioMart or UCSC Genome Browser style browser. If it is an internal project, the script jockeys can help you I'm sure.

BioMart (or the specific Mart for your species if it's out there):

1. Go to BioMart.org
2. Click Martview
3. Select the database and data set.
4. In Filters, set the region. Use this item to enter your list: Multiple Chromosomal Regions (Chr:Start:End:Strand)
5. In Attributes, choose Sequences. You also need to pick a nucleotide box* here, but I'm not sure which for this application.
6. Set and upstream and downstream flank.
7. Click results.

*Although now that I look at Sequences I'm not sure which radio to choose for this purpose. I'm going to have to ask them that. I think I'd choose exon for now.

UCSC: http://genome.ucsc.edu/

1. Go to the Table Browser
2. Set appropriate species/assembly stuff.
3. On Region line, set items in Define Region button.
4. Choose output format = sequence
5. click Get Output.
6. On next page say Genomic
7. Set upstream/downstream length
8. Get Sequence button

Or you can do all of either one from Galaxy (http://www.usegalaxy.org), and you can store that as a workflow you can always go back to later if you need it again. There is also a "Get Flanks" in the Galaxy menu "Operate on Genomic Intervals".

here's a "script-jockey" python solution (untested, but should get you close).

if, in your blast the est is the subject, then you can substitute query with subject and q(start|end) with s(start|end)

import sys
from pyfasta import Fasta

est_fasta_file = sys.argv[1]

# i'll assume it's tab-delimited...
# and est is the query.
est_mirna_blast = sys.argv[2]

# take 100bp up/down-stream.
xstream = 100

est_fasta = Fasta(est_fasta_file)

for line in open(est_mirna_blast):
    # convert to int and 0-based coords.
    qstart, qstop, sstart, sstop = [int(x) - 1 for x in line.split("\t")[6:10]]
    query, subject = line.split("\t")[:2]
    up = min(0, qstart - xstream)
    down = qstop + xstream + 1

    est_upstream = est_fasta[query][up:qstart]
    est_dowstream = est_fasta[query][qstop:down]

    print ">%s_up" % query
    print est_upstream
    print ">%s_down" % query
    print est_dowstream