Can my customers check in for their flight through my portal?

No, in most cases your customers cannot check in for their flight through your portal, because check in stays with the airline and opens on the airline's own website or app, usually a day or two before departure.

What your portal can do is make that step easy for them. Once the ticket has been issued, the confirmation your customer receives carries the airline booking reference and the ticket number, and that is all they need to find the booking on the airline site. Many agencies also add a short line on the confirmation telling the customer where to go to check in, so nobody is left guessing on the day.

There are good reasons this is unlikely to change soon. Airlines ask for passport details, run visa and document checks, and sometimes need the passenger to accept their conditions at check in, and they want all of that done on their own system where it is verified against their own records. A few suppliers do offer a check in or boarding pass feature for a small number of airlines, so it is fair to ask what is available on your plan rather than assuming it is all or nothing.

The practical step is to decide how you want to remind your customers to check in, either in the booking confirmation or as a separate message closer to the travel date, and to make sure the airline booking reference appears clearly on everything you send them.