A late answer 
If your are using SQLITE version 3.7.11 or above, then multiple rows insert is possible by this syntax,  
SIMPLEST WAY
INSERT INTO Rating (rID, mID, stars, ratingDate) VALUES ('207', '102', '5', null) , ('207', '102', '5', null) , ('207', '102', '5', null)
The above clause posted in question do work if the new SQLITE version is used.  
SELECT CLAUSE 
insert into Rating 
        SELECT '207' AS rID, '101' AS mID, '5' AS stars, null AS ratingDate   
  UNION SELECT '207', '102', '5', null
  UNION SELECT '207', '103', '5', null
  UNION SELECT '207', '104', '5', null
  UNION SELECT '207', '105', '5', null
  UNION SELECT '207', '106', '5', null            
  UNION SELECT '207', '107', '5', null
  UNION SELECT '207', '108', '5', null
or SQL is
insert into Rating (rID, mID, stars, ratingDate)
        SELECT '207', '101', '5', null 
  UNION SELECT '207', '102', '5', null
  UNION SELECT '207', '103', '5', null
  UNION SELECT '207', '104', '5', null
  UNION SELECT '207', '105', '5', null
  UNION SELECT '207', '106', '5', null            
  UNION SELECT '207', '107', '5', null
  UNION SELECT '207', '108', '5', null
REMEMBER I you do not want to check for duplicate in above set of inserted values then use UNION ALL in place of UNION as it will be little faster.