Thanks a lot for your answer !
I did some tests this morning and it works.... I don't really understand.
To answer to your questions, my Anker behave normally : blue lights on when I plug it to my Hero 6.
In fact, I can reproduce the red lights blink : if I unplug my Anker (from Anker side) and plug it again, the H6 blink.
To stop the blinking, I have to turn on the H6, then turn it off while charging : then the red lignts are steady. Weird behavior...
Thanks for your help !