SQLite Foreign Key

You need to include the column name before you wrap it with FOREIGN KEY().

CREATE TABLE 
    item (
        _id INTEGER PRIMARY KEY AUTOINCREMENT,  
        checklist_id INTEGER,
        FOREIGN KEY(checklist_id) REFERENCES checklist(_id), 
        item_text TEXT, item_hint TEXT, 
        item_order INTEGER, 
        created_on INTEGER, 
        modified_on INTEGER
    );

You still have to create the column checklist_id INTEGER before you add it as a Foreign key.

So it would be:

CREATE TABLE 
    checklist (
        _id INTEGER PRIMARY KEY AUTOINCREMENT, 
        checklist_title TEXT,
        description TEXT,
        created_on INTEGER, 
        modified_on INTEGER
    );

CREATE TABLE 
    item (
        _id INTEGER PRIMARY KEY AUTOINCREMENT,  
        checklist_id INTEGER,
        item_text TEXT, 
        item_hint TEXT, 
        item_order INTEGER, 
        created_on INTEGER, 
        modified_on INTEGER,
        FOREIGN KEY(checklist_id) REFERENCES checklist(_id)
    );

Simply you are missing checklist_id column in your item table. You need to declare it before you want to set it as FOREIGN KEY. You tried to create FK on non-existing column and this is reason why it doesn't work.

So you need to add this:

checklist_id INTEGER,
FOREIGN KEY(checklist_id) REFERENCES checklist(_id)

now it should works.