Is it permissible to take a commission without the customer's knowledge in exchange for booking flight tickets online?

There is no objection to requesting a commission for a service from the customer, provided that they are aware of this commission. If they are not aware of it, then it is impermissible to take it, because that is considered deception, fraud, and consuming people's wealth unjustly. Allah the Almighty has forbidden this, saying: ﴿And do not consume one another's wealth unjustly﴾ (Al-Baqarah: 188).