Hi, are there any direct flights that go from any of the cycladic islands to the ionian islands?
No, there are no direct flights between these two groups of islands (no ferries either).
You will make your life much easier if you stick to one island group. I understand the temptation, as that was my intention too when I started planning our first trip to Greece. We ended up going to Santorini, Naxos, Nafplio, and Athens. No regrets.