Love the wood suggestion! LOL
We have chainlink all around and have had to come up with some creative solutions. The slats work well, but you can still sort of see through them. They do make one that is supposed to look like green vines and it is pretty dense so it provides more privacy. It would be expensive to do an entire fence but affordable if you are only doing a gate.
I have seen people fasten bamboo to their fence or even a woven beach mat.
My friend wanted to cover her gate, so she bought two inexpensive plastic/flannel backed tablecloths from Walmart in a bright color. She trimmed them to fit the gate and sewed them with the flannel together, so that there was plastic on both sides. then she made ties and sewed them to the corners and I think she put two on each side and one in the middle of the top and bottom. Then she tied it to the gate.