Is there any Daleel for placing one's hand on one's chest after shaking hands with a brother?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

What has been mentioned is part of habits that are inherited from the customs of people.  It is permissible to do so.

There is no harm if someone puts his hand on his chest after shaking hands, and there is no harm if someone does not do so.But the closest to the Sunnah – Allah Knows best – is not to do so, because to our knowledge no one from the Sahabah did so. There is no doubt that if they used to do so it would have been reported to us.

But if not doing so causes antipathy and repulsion among the people who shake hands, then it would be more appropriate to put one’s hand on the chest after shaking hands.

Allah knows best.