There is not a standard definition of a flat file, but the closest thing to a definition I have found suggests:

• Text-only
• No built-in compression
• No index
• Tabular format: one table per file, row-based organization of records
• No metadata: no embedded metadata or schema information
• Unstructured: no hierarchy or relationships between records or fields

My hunch is the flat comes from lack of structure, and the fact than only one table is stored per file (so 2D)