My very first kin, at the ripe age of 9 (or 11?), was Bloody Bunny. I didn't have a term to label it, though, and honestly I never worried too much about it. I just thought what I know realize were my memories was an AU I came up with. Well, I actually had more than one timeline with this kin - specifically the original Bloody Bunny and the Don't Be My Enemy version. Again, I merely thought my memories were AUs I had come up with (unfortunately, I was a very Wattpadbrained child).
I watched Bloody Bunny: The First Blood for the first time when I was 8 and I got hyperfixated on it. I felt very connected to Bloody Bunny - in fact, I even saw myself as them! But, surprisingly enough, The First Blood wasn't one of my timelines. I forgot about it for a year (or maybe a couple of years; my memories of my childhood are very fuzzy), but then I found out about Don't Be My Enemy, which recently got reuploaded onto YouTube with somewhat poorly translated English subtitles. They were still translated well enough so you understood what the plot was, though.
Everyday, after that, I had memories about things that happened during the events of Don't Be My Enemy - including stuff that wasn't shown on screen. Memories of my only friend, who was also my brother, memories of being a man and uncomfortable with being seen as a woman, memories of all the battles I've won, memories of the names of the unamed, so on and so forth. Memories of everything that happened in show and everything that happened in between. Alas, as said before, I thought this was an AU.
It wasn't until later in life, at the ripe age of 12, I found out about being kin, and even then that identity had been dormant for a long, long time. At the time, I thought I was kin with Warden from Superjail, but that ended up just being a fictive in my system. My first memory that I could truly and genuinely identify as a memory due to surrounding myself with people who actually, y'know, knew what being kin meant, was actually one when I kinned Waldo! Which also turned out to be a fictive. DID sure is something.
Then it kinda snowballed from there. Unfortunately, my perception of being kin got kinda warped by the jackasses on Twitter that used D/A and said "I'm [character] irl, not a kin!" My brother in Christ, you literally have memories of your timeline as that character! Thankfully, though, it's been unwarped and I have a better understanding of it. Yay for Neocities kin!
And yeah, that's the beginning of my experience with being kin.
As for the way being kin works for me, I take it very seriously, especially since I view my kintypes as past lives. Being kin is such an important part of my spirituality that it's what my spirituality is built off of!
I view all of my fictionkintypes, therians, etc, as past lives. However, my conceptkintypes and musickintypes are moreso psychological than spiritual, however they're still very important to me.