Hi again, sorry for all the messages, but I've just found this;
https://gbatemp.net/threads/nitro2k01s-sgb-enabler-for-ez-flash-jr.592961/
Basically it's a modified menu kernel that allow the EZ Flash Jr to work almost normally on a SGB.
If you try it, just to be safe, please backup your ezgb.dat from your SD before replacing it with the one from this archive.
Reading this, I think it's normal that the SGB is behaving like a DMG with the EZ Flash Jr, and it's due to the Flashcart not supporting the SGB and thus the game is not able to detect it. I hope this modified kernel will solve the issue