The method to deleting save files has gone through four iterations.
For Gens I-III, simply select “New Game” on the title selection screen.
For Gens IV-V, on the title screen, press Up on the D-Pad, Select, and B simultaneously. When asked if you want to delete all data, select "Yes".
For Gens VI and VII, on the title screen, press Up on the D-Pad, B, and X simultaneously.
For all games on the Switch, go to System Settings --> Data Management --> Delete Save Data. Select the game you would like sava data deleted on. When prompted to confirm, select Yes.
Source: Experience
Hope this helps!
