flexispina has been a recognized Agave name since at least H. S. Gentry's big tome on the Agaves of continental North America. The description is fairly short though but references an to original description in 1920.
However, the pictures in that book do not at all look like the pictures I have seen of A. flexispina in the links on this page - teeth to distinct and huge leaf imprints, nor do the flower stalks match those given in the link provided above... based on looking at that I am starting lean back to thinking this is a form of A. parryi.
Either all the pictures listed with A. flexispina are wrong (I have to say there are some different entries for flexispina on Agaveville that appear different) or there have been some changes since Gentry's book - which is certainly possible.

Based on this website: http://www.agavaceae.com/
The plant we are looking at here does not look like A. flexispina. The presence of marginal teats in flexispina is very distinct from the absence of them in the plants shown here. Also suggests that Agaveville does not have a good entry for flexispina (not looking forward to trying to get that sorted out....)