KitBase 2 will allow you to show the notes fields in the grid (rather than just in tabs at the bottom). That will enable you to use the 'Find' feature to look for key words.
I guess with the sets, it comes down to your way of using them.
If they are a job lot (e.g. a re-arming kit that's a companion to an aircraft) you could just have them as Kit Type of 'Aircraft' and a single Accessory entry (Accessory Type: 'Rearming Kit'?) with notes. Just treat them as an accessory that's not 'with kit' (i.e. in the box with the kit, like you might do with a brass set).
If they are a set that you may cherry pick bits from, you could have a Kit Type of 'Multiple Accessories' or 'Accessory Set' and create individual accessories 'with kit'. That way they'll be listed separately in the kit list (with location indicating they're in the set box) and you can mark them as 'Built' and change the location as you consume them.
Hope this helps.