Some ukes just work better with certain strings. It sounds like Flukes and Fleas prefer nylon. But it also sounds like the black paper works fine. The advantage there is you can easily use nylon if you decide to later. I was out of strings and strung my Kiwaya with a set of nylgut I had and to my surprise, not only did they sound great, they were comfortable to play. So it's possible your tastes will change.
Which strings 'work' is highly subjective to the player, their technique as well as the style of music they play.
Debating
best strings is folly. I can only share what has worked for me.
On 6 different instruments from The Magic Fluke Company, I use fluorocarbon strings exclusively. I never had an issue with the fluoro strings slipping in the nut slots.
I found that of the over 2-dozens sets of different nylon string gauges (from 6 different brands of strings), as well as all variations of nylgut, just sound too dull for me, while also lacking in sustain and dynamic range (both of which I require for my playing style).
Sustain is a critical component of playing in fingerstyle and campanella, and I've found that properly tensioned fluorocarbon strings will deliver 2x-2.5x the time of sustain than all other string materials available for ukulele.
Dynamic range in that the SuperNylgut and NylTech strings have a limited spectrum of soft to loud, in that they have a limit to HOW LOUD they will get during flamenco style strumming. Lots of my own compositions vary WIDELY in dynamic range, i.e. from a whisper to a BANG, and flurocarbon strings, across the board can deliver MORE bang that these other strings
If you only ever strum-and-sing, or just plink out simple melodies, you will likely not notice these subtle differences to fluorocarbon strings. I am not putting down other playing styles as all are valid to the player him/herself.
For my fingerstyle, campanella, and flamenco inspired playing, I
require brightness on the G and A strings to stand out since I carry melody lines on these strings, and with
nylon, these string are typically buried by the boominess of ANY C string, whether nylon or wound.
ALSO:
I noticed that some folks wind their C and E strings from the string hole in the peg, '
out' to the end of the peg so that the string is parallel to the nut slot.
Doing so fails to apply proper angular tension at the fulcrum of the nut slot, which will better hold the string from slipping laterally.
On my own Fluke and Flea ukes, I always wind the strings from the string hole in the shaft, 'DOWN' the tuner peg and TOWARDS the headstock.
This applies the proper angular tension at the fulcrum of the nut slot to hold the string.
So, look how your strings are wound, and try it this way and see if it improves upon the problem.