No, the M3i Zero flashcart designed for the Nintendo DSi does not fit into a Nintendo 3DS (or 3DS XL/2DS).
To run homebrew or backups on a 3DS family system, you need a flashcart specifically designed for the 3DS (e.g., R4i Gold 3DS Plus, Ace3DS X, or Stargate 3DS) running on a compatible firmware version. Modern 3DS hacking typically uses custom firmware (CFW) like Luma3DS installed directly on the system's NAND, making flashcarts largely unnecessary for most users.
Legal Note: Flashcarts exist in a legal gray area. Creating/playing backups of games you own is generally considered fair use in some jurisdictions, but downloading ROMs you don't own is piracy.