You will need Gif editing software. I use ULEAD gif animator so therefore my tutorial will be based around it mainly. You will also need VTFEdit.
1) Open up gif animator. File>new
Set the X and Y to something that's the power of 2. 32, 64, 128, 256. The smaller it is the more frames you will be able to have but you have to make sure your gif fits within the boundaries. Import your gif by dragging it in.
2) File>Save as>Image frames
Change the save type to .png and quality 100. Call it "image" (without the speech marks). Then save it in its own folder
You are done with ULEAD, now you need to open up VTFEdit.
Highlight all of the .pngs you have made and click "open".
Set texture type to "animated texture".
Click OK. Click play to see if it worked.
Then click "info" and check how big the spray is. Anything over 512kb is too much and wont work - if this is the case you must go back to the gif editor and delete some frames or make the gif dimensions smaller.
4) If it worked and you're happy with it. Click Options and make sure "Auto create VMT file is checked".
Save your spray into C:\Program Files\Steam\steamapps\common\team fortress 2\tf\materials\VGUI\logos
and try it out in game!
EDIT: I've created a calculator which allows you to check how many frames you are allowed with different lengths and widths. Found here: Click