What is exactly is KI?
As you can see, there is a lot of controversy about that :-)
Let's start with what it is not. It is not a "life force" or "life energy" (we've known there is no such thing for a very long time now). It is not energy, force, power or any other quantity that a physicist would recognise. Aikido movements can be explained perfectly using very ordinary mechanical principles. Anyone who says ki is "real" in this sense is just plain wrong. If they disagree, then they can build you a ki meter, prove it exists and win the Nobel prize for physics along the way :-)
However, a theoretical understanding and an ability to actually perform the movements optimally are completely different. This is true in every field where movements of your body are required, from playing a piano to bowling a cricket ball to performing irimi-nage.
Giving you a set of differential equations for a set of movements is probably not going to help you learn any of them, for example :-) A lot of what ki is (in the martial arts, anyway), IMO, is explaining things in such a way as to help us actually do them. It's clearer to most people to explain unbendable arm as ki (or water, if you prefer) flowing out through your fingertips, than explain exactly what tension to put in each and every muscle in your arm and shoulder and body etc.
Since a lot of aikido depends on (pretty precise) timing of movements, the concept of "flow" is also often invoked in an attempt to explain how that works.
Most importantly, as any elite athlete will tell you, if your mind isn't right, your body won't work right either. So there are issues about controlling your mind (and therefore your body). Athletes talk about "being in the zone", and you'll hear similar things from martial artists. Then there's controlling fear, "flow" in the sense of moving in harmony with uke (and yourself) and many other things.
So when you talk about ki exercises, I think there are lots of different things that people tend to lump together. Some are physical or biomechanical principles, some are mental.
Be aware that there is a mystical streak in many martial artists, and it is stronger in aikido circles, than, say karate circles. I personally don't find that sort of talk very edifying, and it certainly doesn't make concepts like ki easier to understand. IMO you're better off training with someone who can teach you (as opposed to someone else) well, whether or not they talk about ki.
Ki is just a concept (or set of concepts, maybe). If it helps you, use the concept, if it doesn't, then don't :-)