But this artist makes his own sparking appreciation of their fleeting beauty.

连字符似无必要，删去。

正如网友所言，sparking 是现在分词作 appreciation 的定语。appreciation 与其是“主谓关系”：His own appreciation sparks. 说明“他本人的欣赏是热烈的，热情的”。不应该是“突发的”的意思吧。

结构：make one's appreciation of：对......表示出自己的欣赏。