Minecraft - Can you make a flying potion in Survival Vanilla Minecraft?

I know you can change potion effects with command blocks. I have made a teleportation potion with command blocks. I want flying potions because I want to do a flying PvP with my friend. If you can't have flying potions, how can you make a jump boost and speed boost effect last forever?

Thanks.

P.S: Can you include a seed for a giant plains biome with some forests and waterfalls, lakes, and rivers?

I don't think you can make someone able to fly with a potion, but I know how to make an effect last forever. Just give it a duration of 60000 or something, and when you drink it, it'll say **:**, which means forever, until you drink milk.

No, "flying potions" do not exist.