Note that you don't need to create a primary key for your table. In the absence of an integer primary key, SQLite simply uses an internal key called "RowID" or "OID".
It has all of the features of a normal integer primary key(auto-incrementing, returned by sqlite_last_insert_rowid(), accessible via SELECT, etc), except that it's handled better by SQLite and doesn't require the extra characters in the "CREATE" command.
If you just want a primary key as an auto-incrementing ID for your rows, save yourself the trouble and just use "OID" instead.
Also, according to the SQLite website, the id returned is for the last insert in the current *connection*, not just database. This means that if there are two connections to the same database at the same time, and both perform "INSERT", each can get it's own inserted rowid later, so basically this is thread-safe(So long as no-one calls "REINDEX").