The idea of ​​using a list with sublists works. But there are several issues with your code.

Nested lists must refer to image objects, not strings.

To start generation, you can call the function outside the button command when all widgets have already been created in the root window.

import tkinter as tk
# from tkinter import *
# from PIL import *


win = tk.Tk()

win.iconbitmap(r'pikachu.ico')
win.title('choose your pokemon!')
win.geometry('400x200')
win.maxsize(400, 200)
win.config(bg='red')

# loading alllll images (load gifs once i find out how..)
img1 = tk.PhotoImage(file='poke/1_bulbasaur.png')
img2 = tk.PhotoImage(file='poke/1_charmander.png')
img3 = tk.PhotoImage(file='poke/1_squirtle.png')
img4 = tk.PhotoImage(file='poke/2_chikorita.png')
img5 = tk.PhotoImage(file='poke/2_cyndaquil.png')
img6 = tk.PhotoImage(file='poke/2_totodile.png')
img7 = tk.PhotoImage(file='poke/3_treecko.png')
img8 = tk.PhotoImage(file='poke/3_torchic.png')
img9 = tk.PhotoImage(file='poke/3_mudkip.png')
img10 = tk.PhotoImage(file='poke/4_turtwig.png')
img11 = tk.PhotoImage(file='poke/4_chimchar.png')
img12 = tk.PhotoImage(file='poke/4_piplup.png')
img13 = tk.PhotoImage(file='poke/5_snivy.png')
img14 = tk.PhotoImage(file='poke/5_tepig.png')
img15 = tk.PhotoImage(file='poke/5_oshawott.png')
img16 = tk.PhotoImage(file='poke/6_chespin.png')
img17 = tk.PhotoImage(file='poke/6_fennekin.png')
img18 = tk.PhotoImage(file='poke/6_froakie.png')
img19 = tk.PhotoImage(file='poke/7_rowlet.png')
img20 = tk.PhotoImage(file='poke/7_litten.png')
img21 = tk.PhotoImage(file='poke/7_popplio.png')

# pokemon gen lists
gen1 = [img1, img2, img3]
gen2 = [img4, img5, img6]
gen3 = [img7, img8, img9]
gen4 = [img10, img11, img12]
gen5 = [img13, img14, img15]
gen6 = [img16, img17, img18]
gen7 = [img19, img20, img21]

genlist = [gen1, gen2, gen3, gen4, gen5, gen6, gen7]

counter = 0
def changegen():
    global counter
    if counter == len(genlist):
        counter = 0
    print(counter)
    pokemon1.configure(image=genlist[counter][0])
    pokemon2.configure(image=genlist[counter][1])
    pokemon3.configure(image=genlist[counter][2])
    counter += 1
    gen.configure(text='generation ' + str(counter))

text = tk.Label(win, text='choose your starter pokemon!', fg='white', bg='red', font=20)
text.pack(fill=tk.BOTH, expand=True)

# frame that contains labels
frame = tk.Frame(win, bg='red')
frame.pack(fill=tk.BOTH, expand=True)
# It looks better if your images are the same size.
frame.columnconfigure((0, 1, 2), weight=1, uniform='a') # equal-width grid columns
# The frame is packed in the root window, but the frame's children are ordered by the grid geometry manager.
#       | col 0    | col 1    | col 2
# --------------------------------------
# row 0 | pokemon1 | pokemon2 | pokemon3
# --------------------------------------
pokemon1 = tk.Label(frame, bg='red')
pokemon1.grid(column=0, row=0)
pokemon2 = tk.Label(frame, bg='red')
pokemon2.grid(column=1, row=0)
pokemon3 = tk.Label(frame, bg='red')
pokemon3.grid(column=2, row=0)

gen = tk.Label(win, text='generation 1', font=14, pady=10, bg='red')
gen.pack(fill=tk.BOTH, expand=True)

button = tk.Button(win, text='next gen>', command=changegen)
button.pack(side=tk.BOTTOM)

# At the time we call the function, the variable names are already defined (pokemon1, pokemon2, pokemon3, gen, ...).
print(globals().keys())
# call function to start generation 1
changegen()

win.mainloop()