I have been swimming 1,000 yards non-stop of fly once a week for several months. It is my weekly high. I worked up to it gradually over about six months, after two years of core exercises and swimming at least twice a week year round. I only swim 1,000 to at most 2,000 yards a session. So I am no great swimmer. I am a 58 year-old male, only of slight build, not all that muscular amymore. But maybe a few things that I have learned can help others realize that they too can do this.
The Pull. I start from my hands overlapping in the streamline position. I pull with flat hands, thumbs relaxed wherever they want to be. I end the pull quite early by sliding my hands far out to the sides after the pull. I do not pull far back towards my feet. This saves energy and greatly reduces stress on my shoulders. The hand stroke effort is more than in breaststroke, but not as much as sprinting fly. When I sprint fly, the faster water carries my hands back farher. For distance at a slower speed, I don't have that advantage.
The kick. I only kick once to save leg energy. But I bring my heels up quite a bit first to get good momentum coming down. I kick hard coming down. I end the kick a little bit deep to get my hips up for the glide. My head is down as I end the kick. I can almost see my toes finish the kick as my hips rise up. Hips end up high, head and feet end up down, just a little. I don't mean to exaggerate this, but keeping it in mind helps.
The glide. I glide for less than a second with my hips hopefully still high, head down and hands in the streamline position. All of the muscles in my body completely relax for less than a second to recover, except that I hold my full breath in briefly during this time to give my full lungs time to exchange oxygen/carbdon dioxide. Then I breathe out explosively as I raise my head to breathe. Oxygen/carbon dioxide management is crucial to the distance. Full lungs when possible are important for the distance.
Kinesthetic awareness. I concentrate on my middle finger tips position to help me keep my hands flat with fingers (but not thumbs) together during the pull. I concentrate on my toes' position to help my kicking form. Everything in between works smoothly this way.
Cautions: Work up to the desired distance gradually. Don't do too much and then have to stay out of the pool for two weeks. Quit before it hurts, especially the top of your shoulders. If you have existing shoulder injuries or back problems, this is probably not for you. Core exercises outside of the pool will help a lot. You are different than me. Give yourself time to decide what works for you. I hope you enjoy it as much as me. If I can do it, hopefully you can too!