I have a short answer and a long answer:
The short answer is that wherever some activity related to Delphix is limited by I/O speed, flash storage should improve that process.
The long answer is that there are some instances where Delphix benefits from faster I/O, and other instances where the benefit is negligible.
When the source database is on a server that uses flash storage, JDBC queries between the Delphix Engine and the source database should run faster. Disk I/O should be faster, and the database should, therefore, return results faster.
On the other hand, a VDB is nfs-mounted from the Delphix Engine by the target server. Even if the target server uses flash for storage, I would not expect much benefit, because Delphix holds those data on the DE. With the possible exception of the Delphix toolkit, Delphix performs very little disk I/O on the target server.
I hope this helps, let me know your progress,