I've not used RootsChat before, so forgive me if I don't get this quite right.
The following are the only AYLETT baptisms at Faversham Parish Church between 1620 and 1801, which suggests that Thomas and maybe Susanna moved here from elsewhere, though they could have been born and brought up in a neigbouring parish. Unfortunately I don't have a register transcript between 1801 and 1835 (Civil Registration) but could ask a colleague to undertake a search in the original registers for you, to see if after 1801 Thomas and Susanna also had a son Edward. However if bb. stands for base-born, as I suppose it does, it looks as though Thomas had died by 1793 and Edward would not be his son.
1788 21 03 William s/o Thomas Susanna AYLETT
1790 25 07 Thomas s/o Thomas Susanna AYLETT
1792 18 03 Sarah d/o Thomas Susannah AYLETT
1793 3 11 John s/o Thomas Susannah AYLETT
1797 19 02 Henry s/o Susanna AYLETT bb. Widow
1799 28 07 John s/o Susanna AYLETT bb. Widow
1786 20 05 Hannah d/o Thomas Susannah AYLETT
Several AYLETTs were involved in the Faversham explosives industry, as you may have discovered.
Have you looked at the Faversham website, by the way -
www.faversham.org ?