I saw a video with a marbling technique done on cookies with clear vanilla. Can I use a butter flavoring instead to save money?

I feel your pain about the price of vanilla extract of any color. Your butter extract sounds delicious, but as Gammy notes, its golden color may add a color note that could change the color of your dough. When I make Swiss meringue buttercream icings for cakes, I typically add titanium dioxide (available in the cake aisle of any craft store) as a bleaching agent to pale the color of the butter in the icing so that colors are more true. That way pink is pink rather than salmon, and blue is blue rather than blue-green. I suspect it would be equally helpful with your (delicious-sounding) butter extract.

You know you will get a different flavor using butter flavoring rather than vanilla, which may be fine in your recipe. I would experiment with the gel coloring and standard vanilla extract. The video artist most likely recommended clear vanilla so the color of the gel would not change. With a pastel effect, standard vanilla most likely would add a bit of a tan cast to the gel. Going for a more intense color, there may be no noticeable effect.