Mike
Your question is pretty generic - which slimline kit specifically are you asking about?
Most of the slimline kits I've seen have been described as using 'Cross-style' refills. 'Cross-style' refills refer to a refill design originated by Cross for their twist-style pens. In the broader sense, this refill style is classified in ISOm12757 as 'type C1'. See
https://unsharpen.com/pen-refill-guide/ for a summary of this standard.
The Schmidt catalog does not list type C1 refills. I have a vague recollection of reading somewhere they Schmidt does offer refills in that format, but I can't find anywhere to buy them.
However, it is possible to purchase C1 refills made by Cross, Monteverde, and Schneider, as well as a number of anonymous Asian manufacturers.