Telling the full story so all the keywords will be included in my response for future searchability:

I've been looking everywhere for a driver or chipset info for the unbranded "Mini HD USB 3.0 HDMI Adapter" for years. I finally dug though enough duck duck go results to find a page that claims it uses the Fresco logic USB display driver, which brought me here.

I was able to get the driver to work using Linux Mint 18.2 "Sonya" with linux-headers-4.13.0-45-generic, but the instructions on git hub were not perfect.

1. Clone the repository git clone https://github.com/FrescoLogic/FL2000.git (If you don't have git installed you can install it with sudo apt install git )
2. Navigate to src: cd FL2000/src/
3. Run make (contrary to the instructions, you don't need to edit KERNEL_PATH as the bug was fixed)
4. Insert the module sudo insmod fl2000.ko
5. Change to sample cd ../sample/
6. Run make (I got an error here, but was able to test the driver and see an image despite the error)
7. Run sudo ./fltest 0

This crashed the first time I ran it but worked when I re-ran it a second time. Running it a 3rd time, it hangs my system.

Rebooting with the device plugged into the USB port seems to help. It will work at first launch. However, during shutdown my system is unable to disconnect from it's built in RAMDrive and will hang, ctrl-alt-del will move it a few steps further, but then it hangs again forcing me to do a hard shutdown.

I'm not sure if fixing the error when running make in the sample directory make: /opt/hi3798/arm-hisiv200-linux/bin/arm-hisiv200-linux-gnueabi-gcc: Command not found would make this any more stable.

I googled and came across this thread saying I "need to add head file <sys/ioctl.h>" -- I didn't know how to do that so I followed the recommendation in this thread mentioning I should install some gcc packages:

sudo apt-get install gcc-arm-none-eabi gcc-arm-linux-gnueabi

After installing, make progressed further, but I am now getting a make: /opt/hi3798/arm-hisiv200-linux/bin/arm-hisiv20/opt/hi3798/arm-hisiv200-linux/bin/arm-hisiv200-linux-gnueabi-gcc: Command not found error.

Installing ia32-libs hasn't helped.

It depends on the converter chip and your operating system.

Most USB/HDMI converters sold today contain hardware from either DisplayLink or FrescoLogic.

Short answer:

You will probably get best results using a DisplayLink device and Ubuntu 16.04 or 18.04.

Long answer:

FrescoLogic

There is an official open source driver available at github for the fl2000 chip, but as the readme says:

This driver is tested on Ubuntu 14 LTS as well as some Android platforms with kernel version 3.10.x. This driver source might not compile on newer kernels (eg. 4.0 or above) because of the fast-moving API changes in the mainstream kernel. You might need to adapt it for your own use.

This issue indicates that there is no support for newer kernels right now. So if you aren't using Ubuntu 14.04 anymore, you'd have to wait for someone to port it (or do it yourself). There is also a reddit where a user claims he got it to work on Ubuntu 18.04 Alpha 2, but didn't provide any further information.

DisplayLink

They officially provide drivers for Ubuntu 14.04, 16.04, 17.04, 17.10 and 18.04. The latest driver version is available for 16.04 and 18.04. According to the release notes, they support the following:

G. Supported Features & Hardware

================================

This driver will support up to 2 displays connected to DisplayLink devices. More than 2 DisplayLink displays may work, but not supported or tested by DisplayLink.

Resolutions up to 4K are supported on the appropriate DisplayLink hardware.

Device families supported:

• DL-6xxx
• DL-5xxx
• DL-41xx
• DL-3xxx

DL-1x5 and DL-1x0 devices use the open source udl driver, which is not developed or maintained by DisplayLink.

The driver is not compatible with closed source graphics drivers. If in doubt, take a look at the known issues page.

What you can expect from it

From my own experience, it works well for office use or browsing the internet. In general, everything where the display output is mostly static. You can watch videos, but you'll notice visible artifacts because of the high compression that is needed to be able to transfer the images over (relatively slow) USB3.0. You can't really play 3D games.

You cannot disable the built-in display of laptops (see github issue).

How to tell which hardware is used

The device you linked to uses FrescoLogic hardware. Although most sellers won't include that information in the description, they often provide links to drivers. In your case, they linked to a file called FL2000-2.1.33788.0.exe which indicates it uses a FrescoLogic FL2000 chip.