One way to achieve your goal is to slice-up a colormap and then plot each line with one of the resulting colors. See the lines below that can be integrated in your code in appropriate places.

import numpy as np
import matplotlib.pyplot as plt

# 1. Choose your desired colormap
cmap = plt.get_cmap('plasma')

# 2. Segmenting the whole range (from 0 to 1) of the color map into multiple segments
slicedCM = cmap(np.linspace(0, 1, len(Subjects))) 

# 3. Color the i-th line with the i-th color, i.e. slicedCM[i]
plt.plot(f, Welch, c=slicedCM[Subjects.index(Subject)]) 

(The first two lines can be put in the beginning and you can replace the line plotting curves in your code with the third line of code suggested above.)

Alternatively, and perhaps a neater approach, is using the below lines inside your main loop through Subjects:

cmap = plt.get_cmap('inferno')
plt.plot(f, Welch, c=cmap(Subjects.index(Subject)/len(Subjects))) 

(I see in your question that you are changing Subject when you load the file again into Subject. Just use another variable name, say, data = np.loadtxt... and then f, Welch = signal.welch(data, ..... Keep the codes for plotting with different colors as suggested above and you won't have any problem.)