How can I make the jump on my GIF smoother?

As  much as you increase the number of frames the movement will become smoother and that is for all movements not only the jump . and for the jump movement it is one of animation principles ( anticipation principle )

Theres actually two variables here for fixing the 'Jump' issue: People partially/Scientifically answered the question.  

1) Yes, Checking Frame rate (FPS) on time line. 

2) From my experience (If your aiming to create Looping animation without jerks/Jumps I would copy and paste the first animation Key frame to last Location). This will ensure your 'Basic Position, Rotation and Scale' values match to beginning frame'. 

Creating seamless transition between key frames. 

I hope this helps to getting rid of those annoying kinks. Good luck!

Most computer displays are60hz (60 frames per second). The magic numbers you need for the Frame Delay are:

• 2 frames at60hz =0.th of a second =0.03s frame delay.
• 3 frames at60hz =0.th of a second =0.06s frame delay.

Most of the time, a0.03 or0.06 second frame delay is what you’ll be after.

play with frame rate

I think you need to use curves with ease in and out, it will make your jump look more natural and more real 

Add more numbers of in between &Pay attention to the path of the movement It must be  right

If you add more frames you can make it more smoother animation in your gif file but the file size will be big. so you cahe to reduse the colors. then image quality will be very low.

You need to compile and arrange a series of images in the animation program

There are too many ways to solve that. Icrease frame or there was an option named tween :)

Greater the Number of frams makes video more smoother. So i think it's all about frams per second

There is a option of "Tween animation frame" next to "Duplicate select frames" button, Select the frames and then click on "Tween Animation frame" this will smooth your animation.

Thanks

From my experience (If your aiming to create Looping animation