First let me compliment you on how cute you two loo together!
My situation is a little different from yours, but I think I can help. (I need to explain the situation a bit first) A couple years ago, my trainer was diagnosed with breast cancer. A few months after that, one of my two mares died. My trainer was boarding two horses (a mare and her foal) at the barn where I trained with her. Because treatments were getting so expensive, she would have to sell one of them. Now, it was time to wean the foal, and I needed a friend for my mare, so my trainer moved her horse to live on my property.
Now, I didn't really get along with this horse, until we bought another mare (3 mares now!). A few months later, my trainer passed away, and a week later, a friend of hers from the barn had found a woman to give this mare to.
I felt horrible for saying goodbye to her, until I heard a bit about her only a month later: She had made fast friends with a gelding in her paddock, and was giving lessons to children. This horse was a very good dressage horse, but rather temperamental (to horses and people) , so to me, I was pleasantly surprised to learn that she was making friends.
I guess what I'm trying to say is, think about how much Flynn has taught you, and how much you enjoyed learning from him. It sounds like his owner is a good person (she's retiring him because it may not be healthy for him to jump, due to his age...?) so she'll find him the perfect home. Maybe she'll even give you a little bit of information on his new home, if you're worried about where he's going.
And as for actually saying goodbye, hugs, kisses, and telling him how much he means to you will probably help both of you. Maybe do something that you both enjoy on your final ride, and take lots of pictures.
I know that it's always hard to say goodbye to a horse, but I hope that helps a little bit!