@Reti43 is absolutely right. You will need to save your settings to a file. I put some code together in case you are more of a visual person. For this example, to work you will need to create a file called config.txt in the same folder as your python script.
from tkinter import Tk, Button, colorchooser
import os
root = Tk()
# if config.txt exist open up the config file
if os.path.isfile('config.txt'):
with open('config.txt','r') as f:
# if the config.txt is empty set to default purple
if os.stat('config.txt').st_size == 0:
root['bg'] = '#800080'
#otherwise grab the last color setting. Set root['bg'] to that value
else:
root['bg'] = f.read()
def choose_color():
color_code = colorchooser.askcolor(title ="Choose color")
root['bg'] = str(color_code[1])
# save the color value to config.txt every time color is switched with the button
with open('config.txt','w') as f:
f.write( color_code[1])
button = Button(root, text = "Select Back ground color",
command = choose_color).place(x=400,y=300)
root.mainloop()