Some people have different acceptance levels of what's smooth and what's not. If you look at the TV and movie industry, you will see that a minimum of 24 fps is considered smooth. In the gaming industry, most people prefer 60 fps, which most would agree is the upper limit of our ability to track motion. Having said that, if you wanted to generate a smooth animation, you would need to have a minimum of 24 frames to render in a given second. In your example, your sprite only has 7 frames, which can have two side effects. If you render the animation at 7 fps, then it will have a choppy animation. If you're running your animation at a higher frame rate, then the sprite would appear to be animating very fast. At 30 fps, your animation would loop 30 / 7 = 4 times. This will produce a smooth animation, but you would have to move your character around the screen much faster.
So animation can be broken down into two tasks. First, find out how long it should take to complete a motion. Once you know how long it should take, you can then determine the number of frames you will need based on your target render frame rate. If you need an artist to help you with that, then you'll need to find them. Try contacting the original author of that sprite, or make requests on other sites like deviantart.