The Kensington and Chelsea site has a different configuration to other planning searches - there are 72 applications for InLinks on the site but they don't show up on the InLink Kiosks page.
The field name to search proposals is:
Proposal Keyword
The link:
https://www.rbkc.gov.uk/planning/searches/default.aspx?adv=1&proposal=inlink&batch=20&pgapp=1#tabs-planning-1
will find the applications if you can do something with that.