When mounting photographs on Matt board i use a Hot mount press. They are not an inexpensive item so you could improvise by taking a couple pieces of Matt bored and a sheet of release paper and sandwiching the print between them then using a clothes iron. The release paper goes on the face of the photograph and keeps it from sticking to the mat board and or some of the print bleeding onto the mat board . Check with the local photo framing and mounting store or supplier or by searching online for Hot mount photo release paper and Matt board.
The hot mount press gets to about 200° If I remember correctly, and pressure is applied for about 60 seconds at that temperature to adhere the print to the mat bored with the adhesive paper. ( you will not be using an adhesive photo mount paper )
I would start with the Iron on a medium setting and gently running it back-and-forth on the mat board so that it never sits in one place but is always moving and applying moderate pressure, covering the entire area of the print. It may take a few runs of trail to figure out how long to iron it, and you may not get them completely flat but you will be able to get the majority of the curl out enough that it can sit in the flatbed scanner. You may also want to take the warm prints and sandwich them between a couple pieces of matt board and wax paper between each of the photos and put some books on it to sit overnight.