Can I show my customers how much luggage they can take and let them add an extra bag when they book a flight?

Yes, in most cases you can show the baggage allowance with the flight and let your customer add an extra bag during booking, though how much detail you get depends on the airline and on the supplier behind the fare.

When a flight search comes back, the fare normally carries baggage information alongside the price and the fare rules, so your website can display what hand baggage and checked baggage are included before your customer picks a flight. With full service airlines this is often built into the fare itself, so there is nothing extra to buy. With low cost airlines the fare is usually seat only, and bags are sold as a separate extra that your customer chooses on the way to payment.

Where it gets uneven is the level of detail. Some airlines send a clear allowance that you can show neatly, others send only a short line of text that has to be displayed as it is, and a few send nothing useful, in which case the honest thing is to show the airline's own baggage rules rather than guess. Paid bags are the same story, offered by many airlines and not by others, and with some airlines extras can only be added on their own site once the ticket is issued. A bag that has been paid for usually follows the airline's refund rules and not yours, so it is worth putting that in your terms.

Before you go live, run a few searches on the airlines you sell most, check what baggage detail actually comes back and which of them allow a bag to be added, then decide what your booking page should say when no allowance is supplied.