What game/software are you exporting this for, BleST is not setup in your Blend file?

What do you mean that it's not setup in my blend file? The link is of my model pre export, what I am saying is when I do export it to .smd, the format that I need it in, it looks like https://gyazo.com/f576e958cab97e494df8f11683127f03
I can export this model in say, .dmx, and it works fine, but something with this specific animation or weight paint is causing the leg to distort when it exports to .smd

See the picture. Sometimes the engine matters...
https://i.imgur.com/YrW6bMz.png

I don't think this is a rendering issue

Looking at your blend file the first thing I find is that your armature and your mesh are scaled differently and the rotations are different as well.

https://i.imgur.com/BcOC2kc.gif

This explains why I get an animation like this when I bring the exported smd and animation back into blender.

https://i.imgur.com/B3kd4mO.gif

After applying the Location, Rotation and Scale to the objects so they are all the same, I find that your animation starts on frame 0, when I export the smd again, I end up with the pose coming back into blender like this.

The armature is in a pose but the mesh is in a t-pose. I have to investigate this, this is not right.

https://i.imgur.com/MkPXchw.png

So the reason why the armature is in a pose, but the mesh isn't is that the I had set the pose to rest position before exporting, BleST found the mesh in TPose, but the active animation says the bones need to be in that position and this combination is the ref position for the model.

Both upper leg bone have bone roll in them Leg on the right 84d and the leg on the right -81d (I think these should be 0) like all the others which are set to 0 roll (except the one that has that ball attached to it at the head, it's set to 0.000014d and should be set to 0 as well)

So I created a ref animation in its rest position and made sure that was the active animation on export.
https://i.imgur.com/ooQAX87.png

(I'm getting closer, this is the result of the reimported SMD. )
https://i.imgur.com/hDsBvvc.png

But there is still a problem. Note the way the bones are shrunk and look at the position and length of your root bone and how the leg bone connect to it and are rotated, also look at the position and rotation of the lower leg bones (still investigating)

So, I made a change to your armature, shrinking the Bone bone and pulling the base even with the 2 upper leg bones and I set the roll of the leg bones to 0. The shrinking and moving of the Bone bone was the correct thing to do, setting the roll to 0 was wrong, because you did the walk sequence with the roll set. This is what I ended up with after export.
https://i.imgur.com/oVcmvkr.gif

Setting the rolls back to what they were,

this is what I get after the export.

https://i.imgur.com/SGVHxqq.gif

(Which I believe is what you're looking for.)

https://i.imgur.com/eM9rrap.gif

https://i.imgur.com/Pj5SlbK.png

If you want my edited blend file so you can compare it to yours, grab it here

https://www.dropbox.com/s/ld21y6kgy7d5okx/Melmetal-WALK_pj.blend?dl=0

Let me know if you got it or don't want it so I can delete it from my dorpbox.

I got the file, so you can delete it. While I don't completely understand why the size of that bone would cause that to happen, I do appreciate the time you took to figure out my problem.