Going up is not bad, it is the coming down. Even the fall is not bad, it is the sudden stop at the bottom.
Perhaps I missed it, but I did not see any spring at your connections or any slack in the chain. (It May be there and I missed it). But when the wind begins to blow. The trees will not sway in unison and, if there is no slack or something to take up the variations in tension on the chain and the changing distances between trees, the chain or the securing mechanism might break. I suggest an extension spring at each anchoring point.

Engineer and missionary

Photo by century spring