Hello Pedro Correa de Castro,
Thank you for your interest in NXP kinetis product, I would like to provide service for you.
As you know the KV31 don't have the ROM bootloader, so if you want to use the uart bootloader, we need to use the flash bootloader, the uart flash bootloader actually is a small piece of code which should download to the KV31 at first with the programmer or debugger.
I have test the uart flash bootloader in the kboot2.0 with my TWR-KV31F120M board, it works ok on my side.
Now, please follow my step to try it again, let's take TWR-KV31F120M board as an example, you need to download KBOOT2.0 at first.
1. open KV31 bootloader project in folder:NXP_Kinetis_Bootloader_2_0_0\targets\MKV31F51212
2. Choose tower_bootloader project, build and download it with your debugger.

3. Select the application code which relocate to 0XA000
You can find it from folder: NXP_Kinetis_Bootloader_2_0_0\apps\led_demo\MKV31F51212\iar\binaries\led_demo_tower_a000.bin
4. open KinetisFlashTool in folder:NXP_Kinetis_Bootloader_2_0_0\bin\Tools\KinetisFlashTool\win
5. Configure it like this

COM port should connect your board virtual com port, you can check it in your PC device manager:

Before you click connect button, press the on board reset button at first.
From my above picture, you can find I can download the application file, and after I download it, I can see the on board LED blinking.
Wish it helps you!
If you still have question, please let me know!
Have a great day,
Kerry
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