You could use the field "Usages" for that. (You have to "Show Hidden Fields" first, and then look in the Sense area, near the end of the sense). This is a list item field, so you would need to populate the Usages list in the Lists area with the names of the different regions you want as possible values for that field.
That isn't really what that field is for, but it is one possible use of it.
For the next version of FLEx (8.3.x), we are considering adding a "Dialect Label" field. There would be one version at the sense level and another version at the entry level. It will be a list-choice field, so you will need to populate a list with the possible values for this field. When you make a reference to a word, if it has a Dialect Label, you would be able to make that show on the cross-reference.
We are still working out some of the details about how this will work, so I would be interested to hear from anyone who would use this function.
In the future, we hope to have a more extensive way of tagging nearly any piece of data in FLEx for the dialect, but that is some ways off in the future. This field is intended as a stop-gap measure in the mean time.
-Beth