It’s hard to say. I remember experiencing a pain in the same area when I first started training the back lever. It was simply my body not being strong enough for the move and becoming used to the tension involved. It could also be a sign of improper technique.
I would suggest firstly becoming comfortable with a standard two arm elbow lever before trying the clutch flag. The elbow stab is quite similar and, while the clutch flag is harder, they, like all levers, will entail a similar type of full body tension.
Of course, I must say that there’s always the possibility that you have some kind of biomechanical impingement or otherwise undiscovered medical condition. If you’re concerned about this I’d advocate seeking professional medical advice before continuing any training that causes this sensation.