Is this loft bed flooring strong enough?
2x6 framing would be strong enough, but I have a couple of concerns.


Racking - I think you should put a cross brace on the back (2x4 would be fine)
Mechanical fasteners - for the elevated frame, you definitely want to use either lags or structural screws to attach it to the verticals. The rest can be nails and/or construction screws (largest that don't protrude through the other side).