Is it possible to get items saved on the clipboard on another phone once I login to the keyboard with my account?
Yes2No
Official comment
Deniz K
Hi, you can now sync your copied text across your devices with Cloud Clipboard (This feature is currently available for SwiftKey Beta with 7.8.5 and above only.)
Hi, you can now sync your copied text across your devices with Cloud Clipboard (This feature is currently available for SwiftKey Beta with 7.8.5 and above only.)
How to use Microsoft SwiftKey to copy and paste across your devices – SwiftKey Support
No it doesn't sync data MS isn't Google Keep Notes