Can my customer choose their seat on the plane when they book a flight on my portal?

Yes, in many cases your customer can pick a seat at the time of booking, but it depends on the airline and on the fare you are selling.

Airlines that share their seat maps through the booking API will send back a plan of the cabin showing which seats are free, which are already taken and which ones carry an extra charge. When that information comes through, your portal can display it and your customer can choose a seat before they pay. Low cost airlines nearly always charge for a seat, and many full service airlines now charge for the better seats as well, so the total your customer sees may go up once they make a choice.

There are also airlines that do not open their seat maps to outside systems at all, and some that only open them once the ticket has been issued. In those cases your customer will not see a seat plan on your portal, and the seat has to be picked later on the airline's own site using the booking reference, or at the check in desk at the airport. That is the airline's decision rather than something the portal can force, so it varies from one airline to another and sometimes from one route to another.

If seat selection matters to the trips you sell, check which of the airlines you are connected to actually pass seat maps through, and tell your booking staff to warn customers politely when a seat can only be chosen after the ticket is issued.