I heard of I having been chosen to be the coach of the team.

此句语法错误。of后接动名词复合结构，动名词的逻辑主语要么用属格my, 要么用宾格me. 主格I 为语法错误。

I heard of my having been chosen to be the coach of the team.

to be...为动名词短语中的主语补足语，为动名词的内部结构。整体红色部分为动名词复合结构作介词of的宾语。

这个句子很别扭。改为下句就自然了：

I heard that I had been chosen as the coach of the team.