If this is a record of Robert Kay "being received" where is the record of the "private baptism" that preceded it?
Cromwell's 5 Sep 1538 mandate required all baptisms to be recorded/registered. The rite of "being received" was not in the frame. The "private baptism" was registered plus a flag/indicator to indicate the status of the baptism for later reference. The follow up "being received" did not involve baptism - this was significant.
The Church of England's 1701 publication "The book of common prayer, and administration of the sacraments, and other rites and ceremonies of the church ..." explains the baptismal rite ("public", "private", "being received" and "of riper years" - sadly, nowt about the paperwork to support it!).
The few (very) records that identify "being received" that I have come across show the earlier  "private baptism" with a note against it reflecting this. It depended on the whim of the Minister/Curate performing the rite. But all this is against a background of possibly who cared diddly squat about maintaining accurate registers. Again, if the "private baptism" occurred in a different parish to what extent did the new parish attempt to identify/confirm that the new "baptism" should be a "public baptism" or a "being received"?
If someone can identify the paperwork/recording involved it would be much appreciated.