The next though I had is that the sensor's purpose was to measure the load (A) on a wire, so maybe the sensor is actually making it a flat line already?
I honestly have no clue, this is just me guessing.

Herewith I have attached a schematic diagram of the setup.

For the pyhton codes, I have referred following link https://github.com/OpenLabTools/RPi_ADS1115/blob/master/code/continuous_read_adc.py with some modification. It is mentioned below:

from Adafruit_ADS1x15 import ADS1x15
import time
import numpy as np
import matplotlib.pyplot as plt


pga = 1                 # Set full-scale range of programable gain amplifier 
ADS1015 = 0x00          # Specify that the device being used is ADS1015
adc = ADS1x15(ic=ADS1015)   # Create instance of the class ADS1x15 called adc

# Function to print sampled values to the terminal
def logdata():

    print "sps value should be one of: 128, 250, 490, 920, 1600, 2400, 3300, otherwise the value will default to 1600"
        
    frequency = 1000                    # Data rate in Hz
    sps = 3300                              # maximum sps value for ADS1015 
    time1 = 10                          # how long to sample in seconds
    
    period = 1.0 / frequency        # Calculate sampling period

    datapoints = int(time1*frequency)   # Datapoints is the total number of samples to take, which must be an integer
    dataarray=np.zeros()  # Create numpy array to store value and time at which samples are taken

    adc.start_adc(0, pga, sps)          # Begin continuous conversion on input A0
    
    startTime=time.time()               # Time of first sample
    t1=startTime                    # T1 is last sample time
    t2=t1                       # T2 is current time

    V_dd = 3.3                                      # ADS1015 is powered with 3.3V from RPi
    n    = 12                                       # No. of bits in ADS1015
    senstivity = 0.022                              # Sensitivity of WCS1600 in V/A
    
    for x in range (0,datapoints) :         # Loop in which data is recorded
            
            dataarray = time.time()-startTime                            # Store the sample time in the numpy array            
            dataarray= ((adc.get_last_result())*(V_dd)/(2**n))/ senstivity   # Get the result in Amperes of the last conversion from ADS1015 and store in numpy array


            while (t2-t1 < period) :        # Check if t2-t1 is less then sample period, if it is then update t2
                t2=time.time()          # and check again       
            t1+=period              # Update last sample time by the sampling period
                    
    return (dataarray)

dataSamples = logdata()                       # Call function to log data
    
# Plot time data
TIME      = dataarray[:,]
CURRENT   = dataarray[:,]
plt.plot(TIME,CURRENT 'r', linewidth=1)
plt.xlabel('Time (s)')
plt.ylabel('Current (A)')

The input side the charger reads (110-220 V, 50 Hz, 0.3A).So we can expected a sinusoidal wave for the current time stamp with maximum current restricted to 0.3A.

However, on plotting the time vs current below graph is achieved which is obviously wrong:

Can somebody please let me know why am I not getting sinusoidal waveform, I would be very much appreciative