Nothing is added to the snapshot as it's RO. A flexclone is more or less a full working flexvol and uses an aggr for it's data. The difference is it's using another volume as it's reference point.
Think of it like this.
When you first take a flexclone, there's not really any increase use of space as the clone is just pointing back to the source volume from its data. Once data is added xor changed the flexclone starts to use space, but it's only the difference. If and when you ever split the clone however, it will use the space of the original vol +- whatever has been changed during the course of time it was a clone.
Give this a look over if you have a minute -
https://community.netapp.com/t5/Tech-ONTAP-Articles/Back-to-Basics-FlexClone/ta-p/84874