Flagged email messages not syncing across iPhone and ipad

Most of my email accounts are gmail, and I use the IOS mail app to manage them. I use both my iphone and ipad to read, reply , and most importantly for this discussion, to FLAG individual messages in my inbox. I would expect that flagging a message on my mail app on iphone, would make this appear as flagged in mail app on ipad. THIS DOES NOT HAPPEN. As i wrote in the subject, flagged emails on one device to not appear as flagged on the other device.

A simple check on the above: i open the “Flagged” folder for all inboxes on both devices and I see that there are different emails included depending on which device i flagged them. Or i sort by Flagged on a given inbox and there is no consistency between the devices on which email appear

Could anyone tell me why and is there a way to correct this?