Welcome to the Bunnings Workshop community. It's fantastic to have you join us, and thank you for sharing your question about your slat fence.
I don't recommend disassembling your fence to change the gap between the panels as this might damage them while being taken apart and repositioned. The gap would have to be very small to interfere with seeing through the fence. One way to prevent people from seeing through the fence is to add more panels on the other side to cover the viewing gap.