I found an example online that helped me accomplish this programmatically.
This specific link focuses on opacity which is a property of texture, but its logic can be used for any properties that can be animated, so I was able to modify it to be used for the frame property. Here's a snippet of my code that does it. This all takes place within a script for a Sprite. My particular spritesheet had 4 vframes and 3 hframes. And the particular walk animation I wanted to use was on the 6,7, and 8th frames. An important note is to make sure you use the method to set the animation update mode to Discrete, otherwise you get weird things happening for the walk cycle.
self.texture = load("res://TheSpriteSheet.png")
self.vframes = 4
self.hframes = 3
var walkAnimation = Animation.new()
walkAnimation.length = 0.8
var path = String(self.get_path()) + ":frame"
walkAnimation.track_insert_key(0, 0.0, 6)
walkAnimation.track_insert_key(0, 0.2, 7)
walkAnimation.track_insert_key(0, 0.4, 8)
walkAnimation.track_insert_key(0, 0.6, 7)
walkAnimation.loop = 1
var aPlayer = AnimationPlayer.new()