I am assuming you have some knowledge on exporting meshes from 3ds Max w/ Havok content tools, so I'll be skipping over havok stuff like collision implementation, etc.

Prerequisites:
3ds Max 2013 .
(I can't link you this)

Havok Content tools 2013
(I can't link you this)

Bethesda's Nif exporter.
NifSkope.

Photoshop, Gimp, whatever similar tool of your choice.
A spritesheet of whatever gif you're looking to edit.

Step one, Setting up the spritesheet:

Now the easiest way to do this is use a 2048x2048 or 4086x4086 (2k or 4k)texture. You can use other resolutions like 2048x512, etc, however that requires much more tedium, opposed to the method we're going by here.

Once you have a 2k or 4k template created, get your set of images alligned vertically and in order, all on the left side of the texture space, then export it as an appropriate .DDS format when the above is done.

(There are many online services that can convert a gif to spritesheets.)
https://onlinegiftools.com/convert-gif-to-sprite-sheet

 
(Note: It's very important not have the texture go too far into the middle or else the frames will begin to play out of order.)

Step Two: Preparing the mesh in 3ds Max
Now that you have this done, open the material editor and create a "BSLightingFX material"

 
Once created, drag the scroller down and apply the texture in the diffuse slot and be sure to check the little box on the left to make it visible in the viewport.

 
(If you don't know how / didn't by now, drag the material preview the ball with your BSLightingFX material onto the model in the view port)
(If your material editor looks different, click "modes" at the top, then pick "Compact Material editor")
(Be sure to save frequently)
Now chances are the template might not be lined up properly, and that's totally fine.
 

Just tweak these values until one of the frames is fitted perfectly or best as you can.
(Offset is the positioning U, horizontally V, Vertically)
(Similar for the below scaling, however the texture stretches in whatever direction opposed to simply moving)
 

Here is my end result and values.
(Do note that values will be different for each mesh / texture sheet)

 
Step Three: Animating the mesh

Congrats, you've made this far and I'm sure you'll make it the rest of the way!

With the material editor still open, click your mesh (the part you're animating) then press and hold the little red line near the bottom of your screen and pick the stepped one.
(In your 3ds Max you'll probably have a different one at the bottom, but that's because I had mine previously set up for stepped animation)


 
Once you've done that, select "Auto key"
Then "Set keys"

 
Now that you have "Auto key" and "Set keys" enabled, drag the timeslider to another number, tweak the offset in the material, drag it to another number, then do that until all of your frames are complete.

 
If you run out of frames / space or you have too many, open "Time configuration" and change the amount of frames, and other settings.
(Do note that you should set the frame count to +1 more than you need. So if you need 120, set it to 121, etc.)

 
Once you've set your frames, export your .nif to where ever your mesh should be.
Once done, run your mesh through Elrich 
(Can be found in >Fallout 4>Tools>Elrich)
Then replace it with the converted mesh in the output folder.

Step four, finalising the mesh in Nifskope
Almost done! I'm proud of you, honestly!
Load the mesh in Nifskope, click the animated part, then click the flag on the left.

 
And change "Clamp" to "Cycle"

 
Then click "BsTriShape" and change that flag to "Cycle" just like above.

 
And if all is done properly, your texture should be fully animated once implemented ingame.