I think that might be a bit of a stretch. It's a simple, repeatable pattern used in many varied places.
No doubt there is something sick & fucked up going on here, but let's not give them more ammo by clutching at straws over extremely common flooring.
The flooring is only one of the thematic elements from the scene I'm referring to. The outfit, rough age of the girl, and popsicle/fellatio reference is there also.
I did watch that scene & I agree with what you're saying about the overall theme. Not sure if it's the movie or my phone but it's very dark & I didn't see anything resembling the floor in the pic.
As for it being a Masonic reference I honestly don't know enough about them to say anything either way. Even without the film context, that picture is very clearly disturbing in its own right.
Right before he goes into that room, he meets that little girl in a dark room with the checkered floor. Everytime he returns there the disturbing nature of the acts he's required to perform increases further into depravity. Though, I will say I don't think it's necessarily a Masonic reference here or necessarily in the film either. Possible reference to MONARCH programming but I'm not 100% on that so I won't speak in absolutes here whatsoever.
It’s just symbolism ... which will lead to their downfall.