Sorry you didn't get much of a response on your first attempt to solve your problem. That happens sometimes.
This is just my opinion but I would expect to have better driver support on the stable, hardened Ubuntu 16.04 LTS platform versus something else. I had similar issues trying to get HP wireless printers to work in my Ubuntu environment and resolving those issues took a lot of Internet research. A good place for you to start is http://downloadlinux.net/2016/03/01/how-to-get-install-samsung-ml-2165w-printer-scanner-drivers-for-ubuntu-16-04-xenial-lts-linux/
Samsung makes a point that it does provide some support for Linux but that the level of support and functionality is going to vary from product to product. Which is another way of saying that Linux users are mostly on their own. http://www.samsung.com/us/support/answer/ANS00045346/
I didn't thoroughly research how to get these printers to work since I have no Samsung printers in house to use for testing. But in my HP environment I quickly found out that trying to use CUPS was a dead end. You should be able to print directly via the USB as a connected printer. For wireless printing you'll need to configure the printer to acquire a DHCP IP address and a few other settings. These operations would probably be easier done from a Microsoft machine although in my case, HP provided a Ubuntu tool that worked well.
Once your Samsung printer is properly configured to print in a wireless environment (you may already have that piece working) it's just a matter of adding the printer via system settings->Printers->Add->Network Printer
If this approach fails, I'd try to set things up using a Samba connection which is more complicated but should work ok.
The green light blinking indicates that you at least have some sort of a connection to the printer but that an uncorrupted file transfer is not working. This could be a CUPS issue which is what I experienced and decided to go another route.
You didn't mention installing the Samsung unified linux driver and configurator. http://downloadcenter.samsung.com/content/UM/201205/20120518170921365/EN/english.pdf page 171. You're probably not going to get very far unless you do this.
It's unlikely that your printer "will never work on Linux". However, the degree to which products work depends greatly on how much effort and cooperation Vendors are willing to invest in supporting their Linux customers.
I had a similar issue with my DCP-7055 after upgrading from 16.04 to 18.04. Installed / reinstalled CUPS and used the Brother installation script. Even the scanner worked! Through the looking glass.
My issue was fixed by following the answer here, "18.4 - Printer 'Filter failed'.
Best Answer
Install
hplip-gui
package withsudo apt-get install hplip-gui
and add your MFP from here.According to HP page HP LaserJet Pro MFP m127fw is fully supported.
Do not forget to install HP Driver plug-in with
hp-plugin
.