Hi Tracey
Very well done you!

The new version of FamilySearch is a powerful search tool:
https://www.familysearch.org/#form=advanced-recordsFor example I just visited the above site.
I then made the selection of "Parents" from the drop down field entitled Relationship, then I typed the first names
only of the parents into the parents forenames fields, ie Joshua and Sarah, then I added the values 1793 to 1826 in the date range fields, and typed 'Hastings, Sussex' into the 'Place' field (or maybe I put Hastings, Sussex England), and the results unfortunately only showed the baptisms in St Clements Hastings of two of Joshua and Sarah's children; Elizabeth Slann and Joshua Slann. (Note I did not need to enter ANY surnames).
I have often used this method when dealing with surnames that are easily mistranscribed, however, no result came up for a baptism for your Thomas.
It could be that the baptism record exists but is not legible enough to be transcribed, or it could be that Thomas was baptised to them (or to another couple) but elsewhere, and his surname is mistranscribed, waiting still to be discovered, or perhaps it was the case the record of his baptism, wherever it happened got lost through time.
Of Sussex records on the IGI, I've only heard of Cuckfield IGI records being discriminative over the genders, where up until this new version, we could only find female baptisms for Cuckfield.
So you can test the link at your leisure, trying the possible variations of mis-transcriptions of Slann, like you said, Hann, and then Stann, Kann, SLAN, etc etc, and broadening or changing the areas.
Let us know if you still have no luck (keeping my fingers crossed for you). Bear in mind, if Thomas's father, like himself was in the Dragoons, that he may also have moved around a bit ....
OneBigFamily