Just a brag, but I've nearly eliminated my use of Kleenex since last year. I used to use 2-3 tissues a day, now it's zero most days.
It's ok to go slow. It's weird at first, feels gross or whatever, and the texture takes some getting used to. I just bought the hankies, decided to keep one close at all times, and only use it sometimes, but still used the tissues when I felt like it. Surprise, now that's most of the time. I get 4-5+ uses out of each one and have plenty to last till laundry day.
They're better than Kleenex in many ways, aside from saving the planet. I can keep one in my hoodie pocket and don't have to worry about it disintegrating or ending up in the wash. I also have different color ones for use as napkins.
You can get cheap good quality hankies from Amazon. I haven't found any elsewhere that I've been happy with and that are affordable. It might be a good moral trade-off to go Amazon in this case, because I haven't bought a new box of tissues in months. I'm willing to provide links to the ones I bought if you want. (The affordable ones I got from Etsy are smaller and already unraveling. They have better ones but too expensive for me.)
You can also make them out of old clothes. Iv'e seen advice on what's best to use. Some people really like flannel, say from PJs or sheets. I already did that for making cleaning rags.
It's kind of fun to figure out how to do things differently, how to fix things, make things out of other things, how to use less. It was intimidating the idea of switching my whole lifestyle all at once, and I've found it better to go slow and have fun. Pick one thing and try it for awhile.