I checked the Scalby PRs this morning and only found the 3 baptisms you mentioned: Robert ,Thomas and Thomasin. I checked between 1804 and 1816.
Unfortunately, the EY RO doesn't have Burniston PRs on fiche - I think they might come under North Yorks, although I did notice that there were some entries in the Scalby PRs which gave Burniston as the abode.
Jill