Do you have a charger for the batteries, or just a power-supply?
It sounds like you are using a laptop supply, which would expect a charge-controller inside the laptop: in this case, you must furnish that.
Apologies if I missed something, but I didn't see any mention of a proper lithium-battery charging circuit.

Just a power supply. Reading Dodgydave's comments above leads me to believe that i can connect a power supply (AC Adapter) in parallel with the bms and my amp (load) and that would supply the voltage to charge the batteries and run the amp. And that the bms would cut off power to the batteries when they were fully charged and also cut the batteries off when they are "drained" so that the amp can run off of the power supply. I am trying to understand all of this before i attempt my build and any soldering. I sure do appreciate all your help Perhaps i am going about this all wrong and there is a better solution? I have watched numerous YuTube videos on bluetooth boombox builds and they all use some kind of li-ion battery pack with what they are calling a "charging circuit" and there is only a DC power jack on the build for a 12 volt power supply.

 

Just a power supply. Reading Dodgydave's comments above leads me to believe that i can connect a power supply (AC Adapter) in parallel with the bms and my amp (load) and that would supply the voltage to charge the batteries and run the amp. And that the bms would cut off power to the batteries when they were fully charged and also cut the batteries off when they are "drained" so that the amp can run off of the power supply. I am trying to understand all of this before i attempt my build and any soldering. I sure do appreciate all your help Perhaps i am going about this all wrong and there is a better solution? I have watched numerous YuTube videos on bluetooth boombox builds and they all use some kind of li-ion battery pack with what they are calling a "charging circuit" and there is only a DC power jack on the build for a 12 volt power supply.

Here is my thinking.
It's not real clear what all your BMS does, but most protect from shorts at the load -- in this case your boom box. Shut off the load from the batteries when they are discharged to about 3 volts each (12 volts total) and balance the cells - allow each to charge to 4.2 volts.
The way most of the balancers work is to "steal" some power from the battery when it reaches 4.2 volts so it doesn't get over charged while the other cells in the pack are still charging. There is a circuit for each cell. So the problem is this: when all the cells are at 4.2 volts that is only 16.8 volts. But you power supply is 19 volts so two bad things may happen. The BMS will get hot and the batteries will still over charge. Think fire.
If you can set the voltage to 16.8 volts this problem goes away but charge time may increase as charge current goes down as the cells approach 4.2 volts.
The other thing the charger worries about is the maximum charge current. This may not be a problem or the batteries may draw more current than your power supply can provide making it get hot.
In general your power supply or charger needs to be able to power the boom box by itself.
So what we could do is build a regulator to drop the 19 volts to 16.8.
What we should find out is the current rating on the laptop supply and the maximum current for the boom box.

 

Will i get 16.8 volts to my amp or 19?

The nominal voltage is usually 3.6V per cell - for charging; some early cells shouldn't be charged above 4.1V, most current types require 4.2V but I've seen a datasheet for a type that should be charged to 4.3V.

In every case; the full charge terminal voltage is critical - make sure you correctly identify the cell type and check the datasheet for correct terminal voltage. If you exceed that voltage; the cell can vent with flaming gas!

Any series chain of cells requires cell balancing so not any cell in the chain charges above the specified voltage. You can buy charging packs that do this - don't try DIY unless you *REALLY* know what you're doing.

Its much easier to design a single cell charger, the cheat's way out is to design around a single cell and a boost SMPSU.

 

what about a 16.8v power supply. Would that do the job?

There is an ideal charging system and there is a 'good enough to work' one of which I get the impression you are looking for good enough to work design which ,yes, a constant voltage source with some sort of current limiting will do the job.

Your battery pack will charge directly feeding the 16.8 volts to the it while the BMS is handling the individual cell voltage control provided the 16.8 volt power supply has some degree of current limiting to keep it from overheating the batteries and or itself at high current draw times like when the batteries re near dead.

 

Here is my thinking.
It's not real clear what all your BMS does, but most protect from shorts at the load -- in this case your boom box. Shut off the load from the batteries when they are discharged to about 3 volts each (12 volts total) and balance the cells - allow each to charge to 4.2 volts.
The way most of the balancers work is to "steal" some power from the battery when it reaches 4.2 volts so it doesn't get over charged while the other cells in the pack are still charging. There is a circuit for each cell. So the problem is this: when all the cells are at 4.2 volts that is only 16.8 volts. But you power supply is 19 volts so two bad things may happen. The BMS will get hot and the batteries will still over charge. Think fire.
If you can set the voltage to 16.8 volts this problem goes away but charge time may increase as charge current goes down as the cells approach 4.2 volts.
The other thing the charger worries about is the maximum charge current. This may not be a problem or the batteries may draw more current than your power supply can provide making it get hot.
In general your power supply or charger needs to be able to power the boom box by itself.
So what we could do is build a regulator to drop the 19 volts to 16.8.
What we should find out is the current rating on the laptop supply and the maximum current for the boom box.

What if I used a power supply AC adapter equal to the total voltage of the pack? Say a 16.8 v supply for a 4S or a 12 v for a 3S? Would that eliminate any issues of fire?