Kissing the hand of one's father or mother, or paternal or maternal uncle, or a shaykh - if it is done by way of showing respect - is permissible and there is nothing wrong with it, so long as it does not lead to any obvious mischief, in which case it is disallowed because of the mischief.
Al-Bahooti (may Allah have mercy on him) said in Kashshaaf al-Qinaa (2/157):
It is permissible to kiss the hand or the head as a sign of religious devotion, and to show respect and honour, so long as there is no possibility of provoking desire.
What appears to be the case is that it is not permissible if it is for some worldly purpose, in which case it is not allowed. End quote.
It says in al-Mawsooah al-Fiqhiyyah, 13/131:
It is permissible to kiss the hand of a pious scholar or just ruler, and to kiss the hands of one's parents, teacher or anyone who is deserving of respect and honour. It is also permissible to kiss the head and forehead, and between the eyes. But all of that applies only if it is done by way of showing respect and honour, or love when meeting and parting, as a sign of religious devotion and a sign of respect, so long as there is no possibility of provoking desire.
Ibn al-Battaal said: Maalik disliked kissing of the hand, and he rejected what was narrated concerning it. Al-Abhari said: Rather Maalik disliked it if it was done by way of undeserved veneration and showing humility towards an arrogant man, but if it is done by way of drawing closer to Allah, because of a person's religious commitment, knowledge or high status, then that is permissible. End quote.
Shaykh Ibn Uthaymeen (may Allah have mercy on him) said:
There is nothing wrong with kissing the hand to show respect to one who is deserving of respect, such as one's father, a shaykh, or a teacher, unless there is fear of harmful consequences, namely if the one whose hand you kiss will be filled with self admiration and think that he is of high standing; in that case we would disallow it because of this negative consequence.
End quote from Liqa' al-Baab al-Maftooh, 177/30
Ibn Jibreen (may Allah have mercy on him) was asked:
What is the ruling on kissing the hand? What is the ruling on kissing the hand of a person who has status, such as a teacher and the like? What is the ruling on kissing the hand of paternal and maternal uncles and others who are older?
We think that this is permissible if it is done by way of showing respect to parents, scholars, people of virtue, and elders among relatives and the like. Ibn al-Araabi wrote an essay on the rulings on kissing the hand and so on; please refer to it.
If this kissing of the hand is done for older relatives and people of virtue, then it should be done by way of respect and not by way of showing humility, and it should not be done by way of veneration. We have seen some of our shaykhs objecting to that and not allowing it, and this attitude on their part appears to come under the heading of humility, not by way of deeming it haraam. And Allah knows best. End quote.
Based on the above:
There is nothing wrong with kissing the hand of your paternal or maternal uncle, if that is done by way of showing respect and honour.
And Allah knows best.
Reproduced from Islam QA