Yes, flatwound strings will definitely help to reduce finger noise. You could also try reducing the top end response of your amp by reducing treble or turning off the tweeter if your cab has one.
Another alternative worth trying is a low-pass filter such as the one in the Hotone GATE pedal. However, when you are using the Markbass Minimark, trying turning up the VLE control, as this is just a variable low-pass filter so should have the same effect.