@minniesBFF I just happened to be on the game's Facebook this morning hoping for an update and I saw this comment & reply from the developers:
https://www.facebook.com/DisneyMagicKingdoms/photos/a.625533104279824.1073741828.545267055639763/761879060645227/?type=3&comment_id=762356017264198&comment_tracking={"tn":"R9"}
The person asked "Hi , Disney Magic Kingdoms, is there a way that I can move my account from a Windows phone to a Android phone?" and they replied with "Hi, progress transfer is possible only between Windows pc-Windows mobile and Android-iOS"
So, it seems that if you're on a Samsung phone running Andriod, that you can have your progress trasfered to iOS!! I'd say just send a ticket in to the "Customer Care" section of the help screen and they can transfer it for you. I also like
@Pheran comment - make sure you also connect to facebook before you turn in your old phone. Good luck!