Danny,

I can't quite make out the words, maybe someone else can help with that,
but I think it's just saying he had a parish license to perform the baptism.

Paige

"de Dni. Parochi liz.a"- Abreviaturas en Latín

"de Domini Parrochi lizencia" - "con la licencia del Señor Párroco"

(which means "with the licence [or permission] of the Parrish Lord [priest]"