Yes,Djinn can incarnate as humans,but I think that the reason why you feel so connected to them and have psychic powers is that you might have a relative who was a Djinn,you might be part Djinn rather than a reincarnation,which is actually rather interesting,I hope I helped,XD

Just like any other being in existence, a Djinn can reincarnate when it is time for them to move on. I've had many past lives, the strongest being a Fallen Angel and a magick user (I have no actual information on whether he was sorcerer or witch) from Atlantis. Both of these are a huge part of who I am today as a practicing witch of 20+ years and spirit keeper. With all of the energies and spirits in this world, it is no surprise that some choose to reincarnate as a human. Most will go through their human life without so much as having a clue while others will feel uncomfortable and lost. I have yet to fully understand if its a good thing that we do find out as it can leave a longing for what we once were.

There is always the possibility that the person might not even be a particular being, but had a great deal of interest in them in their past life and it could be a residual feeling of wanting to know more. Or, perhaps, they could have a mixture in their bloodline. A lot of times we want to know what we don't understand, though it does leave us afraid. It's a hard lesson to get over and can translate through lives. I have a lot of vampires in my bloodline, my connection to them is strong, but at the same time, I want to learn more about this fallen angel from so long ago.

It's believed that within the soul is a core, and a djinn's core usually takes the form of a fire, either blue, green, etc which defines which type of djinn they are ifrit, Maarid, and so forth. In my personal experience with "soul readings" via projection into the manifested landscape of the individual, I come to believe otherkin truly are a real thing just not entirely common. Past lives are vessels our souls choose to live but the soul has had an original form prior to the reincarnation cycle. Some as Humans, some as Angels of different faiths, demons of different faiths, therians, dragons, Immortals, so forth. I just don't believe it's really common.