Once you have the sqlite module installed you could write a python script to "SELECT" your data from the sqlite3 file. If you use a script input in Splunk, your script just just needs to output something like that to the screen:
2014-06-24 14:00:12 +10:00, table="table01", columnA="value from clA row1", columnB="value from clB row1"
2014-06-24 14:00:13 +10:00, table="table01", columnA="value from clA row2", columnB="value from clB row2"
Make sure you handle the exceptions on your script and output errors to stderr so it won't index those messages.