Answer
Wa `alaykum As-Salamu waRahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
There is nothing wrong with giving zakah to brothers and sister if our duty towards them will not be waived.
The late Muslim scholar, Sheikh Ibn `Uthaymeen, states:
If giving zakah to your brother or sister means that your duty towards him/her will be waived, such as if it is obligatory for you to spend on his/her maintenance, but you give him/her zakah so that you save your money and do not spend on him/her, then this is not permissible, because zakah cannot be paid to protect wealth.
But if it does not mean that your duty towards him/her will be waived, such as if it is not obligatory for you to spend on his/her maintenance, because you will not inherit from him, or because you cannot afford to spend on him/her as well as your own family, or you are giving him/her money to pay off a debt that he/she owes but cannot pay off, then it is permissible for you to give your zakah to him/her, rather it is preferable for you to give it to him/her rather than anyone else, because giving to him is both an act of charity and upholding the ties of kinship. (Majmu` Fatawa Ibn `Uthaymeen, 18:422-423)
Almighty Allah knows best.
Source: www.islamqa.info.