Life safety is the primary issue here. A failure during a pneumatic test can be as destructive as a bomb going off due to the large amount of energy stored in the compressed air or other medium; a hydrostatic test is safer in this regard.

ASME Pressure Vessel Code Section VIII Div 1 Appendix 2 provides rules for design of flanges. You can find some links to freely-available design spreadsheets by searching Eng-Tips (try the ASME or Boiler/Pressure Vessel forums) or do a Google search.

The thickness of the flange is a function of the bending moments produced by the gasket reaction forces, bolting forces, pressure end forces, etc, so the layout and size of bolts also enters into this. It is not a trivial problem.

You should be able to buy a rated blind flange from a steel pipe manufacturer.  If you're the nervous type, specify one with a higher rating than your test pressure.  Your pressures (200 psi) and size (16 in.) are not excessive.
I'd would not recommend designing this from scratch.  If you want to feel involved, check the manufacturer's design.