Airways on charts
 

On the charts some Airways say "Nxxx A FL65+", then underneath "(MNM ALT 5500')".

So what's the max altitude you can fly VFR underneath them crossing at 90 degrees without getting filed?

The base of the airway is the higher of FL65 or altitude 5500 ft. The latter is only likely to be higher when the QNH is below about 980 hPa.

So you can do the 90-degree across thing at FL65 if you want to, or you can do what you want at FL64.9 and below!