Thanks to Bryan Oakley's solution :
from tkinter import *
#------------------------------------
def addBox():
row=root.grid_size()
row = row[1]
ent = Entry(root)
ent.grid(row = row,column=0)
ent1 = Entry(root)
ent1.grid(row = row, column=1)
all_entries.append(ent)
all_entries.append(ent1)
#------------------------------------
def showEntries():
for number, ent in enumerate(all_entries):
print (number, ent.get())
#------------------------------------
all_entries = []
root = Tk()
showButton = Button(root, text='Print Text of each Entry Box', command=showEntries)
showButton.grid(row=0, column = 0)
addboxButton = Button(root, text='Add Entry Boxes', fg="Red", command=addBox)
addboxButton.grid(row=0, column = 1)
root.mainloop()