Good concept, could become as famous as flappy bird.
- I would allow double jumps only as COLLECTIBLES (like the burgers), meaning that you have to collect an item that allows you to perform one double jump.
- Jumping in general should not cost stamina. At the moment, the character can not jump at all, but only fly, at least it feels like it. Jumping should have a different animation and maybe even different physics than flying, to allow the player o distinguish between what he is doing. This will also avoid the player to stop holding the button pressed "because I thought I still have my double jump" and then falling down instead "oh **** it seems I didnt have my double jump any more ...", which is the biggest reason why I fell (This - missing a platform by unintentional button release (because thinking you could still jump again)- shouldn't be the main reason for falling but currently is, at least for me - it feels wrong. The reason for missing a platform should be a players wrong timing of the button release when he willingly wants to reach a platform by landing)
- I would not allow flying from start, first you would have to collect a burger. (Why this? This looks like flappy bird. Flappy bird can do "everything" from the start. If a player assumes he can do "everything" from the start, it means that he will not try to discover new things. This way, you will loose players that do not run for points but want to discover something.)
Especially if it gets faster, seeing more would be a benefit, but also generally speaking I would recommend using this:
https://www.google.com/search?q=film+vertically+gif&rlz=1C1GGGE_deDE883DE883&source=lnms&tbm=isch&sa=X&ved=2ahUKEwiEj_qxy6bpAhWOKZoKHf4KAgkQ_AUoAXoECGMQAw&biw=1920&bih=969#imgrc=MCEoEuFZddCNuM
After all, I do not really appreciate the idea of the game becoming faster, for it breaks the players game learning mechanism. Instead, make the landing surfaces a bit smaller and add further traps (occasional spikes above that prevent you going up too far, monsters etc). This way you will contribute to the "discovery" part of your game (new enemies oO I wanna see what else is coming up!) and therefore to its replay value.
;)