Use 'Flat' paint on top of 'Eggshell gloss'?

would be better to lay a primer first. As most latex gloss paint has silicon or other high shine addition that will cause the "flat" paint not to adhere very well. Or you can just sand lightly on the walls to rough out the smoother gloss finish.

Thanks

In order for the paint to adhere properly to the wall, you will need to wash the walls and then lightly sand them down. Wipe or vac all dust from room before you paint.

TSP the walls and then paint your brains out.

magic; flat walls, covers nicely

You probably can do it but the wall will not look perfectly flat on the first coat.