Look at it this way. Cut open a 3 cell flashlight. If you put the negative (black) meter lead on the spring at the butt and put the positive (red) lead on the pos terminal of that end battery you will read 1.5VDC. Now move to the pos of the next battery. You will read 3VDC. Now move to the pos of the 3rd battery. You will read 4.5VDC. Now move to the switch. You will still read 4.5VDC. Now, with the switch off, move to the other side of the switch. You will read 0VDC. There's the break in the chain. Now turn the switch on and you get 4.5VDC on the switch. Move to the bulb and you get 4.5VDC. Move to the other side of the bulb and you get 0VDC because both meter leads are on the negative wire. Forget about all the beep testing and continuity. You are looking for voltage and where the break in the chain is. The 2,20,200 on the meter is the maximum you expect to see on the circuit. Make sure AC/DC is switched correctly. Batteries will always be DC. Other circuits can be AC or DC. Look in the manual to see what spec is for the circuit you are working on.
Here's a few more scenarios. Put a piece of paper between the spring and the 1st battery. Now do the test above. You get 0VDC, when you know the battery is 1.5. Now you know there's a break on the ground side. Now take the paper out and put it between the 2nd and 3rd battery. Now test. 1.5, 3, 0. So, you know the break is between the 2nd and 3rd battery. Starting to make sense now?