use of kindly
Kindly need your help to liase with HR division for getting their support due to the request from Bank related to my application

Question

Answer

No. Generally it's used for them being kind(ly) rather than your need being kind.

Kindly offer your help to liase with HR division for getting their support due to the request from Bank related to my application.
Worded as "kindly" probably means "do it".
.
Kindly help us with this.
.
We are stuck. It would be great if you could kindly help us.
for example
Could anyone kindly explain this to me?

Answer

I would like to request your kind assistance with liaison with HR Department.