I thought there was no solution because I thought the arrow pointing on the line from the flower meant you could only go that direction from the flower, but the solution relies on someone behind able to move backwards from the flower.
Granted there is the blue feedback if you are on the flower, but it’s confusing when you are trying to plan ahead.
Funnily enough I understood all the rules, but still was mentally blocked for a while because I just didn't even consider moving back from the flower as a possibility. I guess there was something about that arrow that was very enticing.
I followed the arrows too. Took me 15 mins or so to solve. I think the former comment meant that he thought that once you are on a node that is in front of an arrow, you have to follow that arrow, but that is not its meaning obviously.
Granted there is the blue feedback if you are on the flower, but it’s confusing when you are trying to plan ahead.
edit: Fun puzzle though!