Usually, we use volume snapmirror to migrate volumes between controllers. Although aggr copy might be easier since the clones would come over without having to mirror them individually. aggr copy does not have in incremental update option though so you need downtime during the copy unlike snapmirror which would be downtime just for the incremental transfer. Prior to ONTAP 8.0.1, you can mirror each flexclone, except you would have a full copy on the target so it wouldn't be unsplit like the source. In 8.0.1, there is a nice feature that was added to ONTAP 8.0.1 to allow snapmirror between two flexclone volumes. If you can use 8.0.1 on both source/target system, this may be the way to go with the least downtime prior to cutover.
To keep unsplit clones on the target... If you can upgrade to 8.0.1, I would recommend you use SnapMirror (and some more commands than just aggr copy, but worth doing for less downtime). If you can't upgrade to 8.0.1, then aggr copy -S looks like your best bet.
From the release notes http://now.netapp.com/NOW/knowledge/docs/ontap/rel801/html/ontap/rnote/frameset.html
Support for SnapMirror relationship between two FlexClone volumes
Data ONTAP 8.0.1 and later support SnapMirror relationship between two FlexClone volumes.
The SnapMirror relationship between two FlexClone volumes that have the common base Snapshot copy helps in establishing a SnapMirror relationship without transferring the common Snapshot data again to the destination system.
For more information about SnapMirror relationship between two FlexClone volumes, see Data ONTAP 7-Mode Data Protection Online Backup and Recovery Guide.
Basically, create the flexclone on the target after you mirror the base volume...use the same snapshot as the source clone. Then when you snapmirror from clone to clone, you won't recopy all the data and you have an unsplit clone just like the source. From the online data protection guide for 8.0.1 (onlinebk.pdf)
Setting up SnapMirror relationship between two FlexClone volumes
The SnapMirror relationship between two FlexClone volumes that have the common base snapshot helps you to achieve a SnapMirror relationship without transferring the common snapshot data again to the destination system. Both the FlexClone volumes should be created from the SnapMirror source and the corresponding SnapMirror destination volumes with a common base snapshot.
About this task
Setting up a SnapMirror relationship between the two FlexClone volumes does not consume any extra space on the parent aggregate for shared snapshots. In this way, you save disk space and network resources. If you delete any of the inherited snapshots from the parent system or transfer new data from the SnapMirror source clone to the SnapMirror destination clone, additional disk space is consumed.