In one of the most distinctive traditions of the Little New Year is the burning of a paper image of the Kitchen God, dispatching the god'spirit to Heaven to report on the family's conduct.

tradition可以是可数名词，也可以是不可数名词。本句为可数名词用法。

我认为句首的介词in属于多余，应该删去，直接用one of...作主语。

One of the most distinctive traditions of the Little New Year is the burning of a paper image of the Kitchen God, dispatching the god's spirit to Heaven to report on the family's conduct.

《韦氏高级词典》有类似用法的例句：

One of our town's time-honored traditions is to have an Easter egg hunt the week before Easter.

只不过本句的表语不是不定式，而是名词化的动名词burning，但和词典例句的结构是相同的。

句子还可以做如下改动：

Among the most distinctive traditions of the Little New Year is the burning of a paper image of the Kitchen God, dispatching the god's spirit to Heaven to report on the family's conduct.

此时，句首的介词短语为表语，表语前置后导致完全倒装句，主语位于句末。

dispatching...显然是现在分词短语，写这个句子的人本意是想让这个现在分词短语修饰动词burn, 作burn的伴随状语。但作者用了名词化的动名词，现在分词dispatching就无法修饰名词burning了。因为现在分词修饰名词为定语，被修饰名词必须在逻辑上是现在分词动作的施事者，但实际上dispatching的施事者并不是burning，而是动词burn的施事者。所以这里出现了语法错误。改正的方法是，将名词化的动名词burning改为动名词burning或不定式to burn, 这样，现在分词短语dispatching就可以做动名词或不定式的伴随状语了。修改如下：

1 One of the most distinctive traditions of the Little New Year is to brun/burning a paper image of the Kitchen God, dispatching the god'spirit to Heaven to report on the family's conduct.

2 Among the most distinctive traditions of the Little New Year is to burn/ burning a paper image of the Kitchen God, dispatching the god's spirit to Heaven to report on the family's conduct.

由于用动名词作表语或主语，易于与现在进行时混淆，所以最好用不定式to burn。