Jumping takes practice. Try this:
You need to first hit one of the directional keys and immediately follow up with your spacebar. Just hitting the spacebar makes you leap in place. I keep my ring finger of my left hand on the #1, middle finger on #2, index finger on "W"and my thumb on the spacebar. I hit "W" and very quickly follow up with my thumb. My index finger goes back-and-forth between "W" and "S".
Good kitty! ...There are also 2 treasure chests, one next to the flower and one in a corner...
Once you make it to the first chest by the flower:
...inspect the back side of that chest. You'll find a button there which materializes a platform that enables you to reach the 2nd chest.