How can I build deck stairs flush with the end of the deck?
Double beam the ledger, 
Notch out a rail seat .65 inches,
Set stringers in place,
Pre drill 3/4" pocket hole horizontally from stringer into ledger (will need 12" to 14" auger bit),
Use 1/2" structural screws to secure stringer to ledger,
Plug hole with hole plugs or mix sawdust with sandable titebond glue and patch hole. 

Additionally, stringer 14ga prebent metal underneath each stringer, stubby nailed to ledger will help support weight if it's high off the ground.