Simon, thanks for the tipps. I will have a look.
In parallel to frustrated playing with the BMP on the Bluepill I tried your approach with the ESP8266, and downloaded the referenced .bin files.
But first of all, the .bat didn't work. But I managed to flash using Esptool directly, and it went through. 
However, I strained my eyes to find a Blackmagicprobe network.
No network. I tried on a bare ESP8266-01 and on a Nodemcu.
However, surprisingly sometimes by chance I saw a connection to some 192.168.... server. But I could not reproduce. How to connect to the ESP assuming that some version of BMPprobe is running unrecognized?
Has the network been removed? 

Output:
G:\ESP8266_BMP_NoOTA_Default>UploadToESP8266.bat
Identifying Tools....

Package Folder Found
[C:\Users\Meister\AppData\Local\Arduino15\packages\esp8266]

ESPTool Found
[C:\Users\Meister\AppData\Local\Arduino15\packages\esp8266\hardware\esp8266\2.7.4\tools\esptool\esptool.py]
-----------
Type the COM Port Name and press ENTER    (e.g. COM10)   :   COM8
usage: esptool [-h] [--chip {auto,esp8266,esp32}] [--port PORT] [--baud BAUD]
               [--before {default_reset,no_reset,no_reset_no_sync}]
               [--after {hard_reset,soft_reset,no_reset}] [--no-stub]
               [--trace] [--override-vddsdio [{1.8V,1.9V,OFF}]]
               verify_flash,erase_flash,erase_region,version}
               ...
esptool: error: too few arguments
Issue Encountered during Upload
Due to the Error Encountered this script will now exit

It is a Nodemcu Amica,
(base) G:\ESP8266_BMP_NoOTA_Default>esptool --chip esp8266 --port COM8 --baud 921600 --before default_reset --after soft_reset write_flash -z --flash_mode dio --flash_freq 80m --flash_size 4MB 0x0000 %CD%/bootloader/bootloader.bin 0x10000 %CD%/blackmagic.bin 0x8000 %CD%/partitions_singleapp.bin
esptool.py v2.8
Serial port COM8
Connecting....
Chip is ESP8266EX
Features: WiFi
Crystal is 26MHz
MAC: 60:01:94:0b:a5:df
Uploading stub...
Running stub...
Stub running...
Changing baud rate to 921600
Changed.
Configuring flash size...
WARNING: Suspicious segment 0x60000014, length 8
Compressed 5632 bytes to 4466...
Wrote 5632 bytes (4466 compressed) at 0x00000000 in 0.1 seconds (effective 703.5 kbit/s)...
Hash of data verified.
Compressed 499328 bytes to 364310...
Wrote 499328 bytes (364310 compressed) at 0x00010000 in 5.3 seconds (effective 749.0 kbit/s)...
Hash of data verified.
Compressed 3072 bytes to 83...
Wrote 3072 bytes (83 compressed) at 0x00008000 in 0.0 seconds (effective 1755.7 kbit/s)...
Hash of data verified.

Leaving...
Soft resetting...

See also this running from c-drive:
(base) sp8266\hardware\esp8266\2.7.4\tools\esptool\esptool.py --chip esp8266 --port COM8 --baud 921600 --before default_reset --after soft_reset write_flash -z --flash_mode dio --flash_freq 80m --flash_size 4MB 0x0000 %CD%/bootloader/bootloader.bin 0x10000 %CD%/blackmagic.bin 0x8000 %CD%/partitions_singleapp.bin
usage: esptool [-h] [--chip {auto,esp8266,esp32}] [--port PORT] [--baud BAUD]
               [--before {default_reset,no_reset,no_reset_no_sync}]
               [--after {hard_reset,soft_reset,no_reset}] [--no-stub]
               [--trace] [--override-vddsdio [{1.8V,1.9V,OFF}]]
              h,verify_flash,erase_flash,erase_region,version}
               ...
esptool: error: too few arguments
Don't know how to fix it, what are the { } meaning?

Thanks for the information.

The command in the script relies on it being run, from the directory where the BIN files are (this is what the %CD% does in the command).

The output here is just stating all possible options to the ESPTool script, and only shows if some of the parameters are missing or incorrect.

From the output so far, I see no problem with the script, as long as the ZIP has been extracted first (as shown in the previous post where the flashing worked fine with the same command)

Does the blackmagic_* WiFi now show up now the board has been programmed?

Had seen the power requirements.
No network, tried big 5V battery, 6V 1.4 A power supply.

Thanks for the update on this, and glad its all up and running now.