In your case the vendor blindly uses a computer program to calculate pressure drop and is embarrassed to admit they don't know how to do it manually. Even worse is that they won't help fix the problem, whose solution could be selling you more trays. I suggest you get a better vendor that wants your business. If so this problem is also a poor reflection on the state of chemical engineering in industry.
Downcomer flooding is when liquid from the tray below backs up to the tray above. For backup flooding this is because the pressure drop across the tray is greater than the liquid head available from the tray spacing. The formulas to calculate pressure drop area readily available in Distillation Design by Henry Kister, Perry ChemE Handbook, and Unit Operation of ChemE by McCabe, Smith, & Harriott among others. You shouldn't have any problems calculating this on your own and it will be an empowering experience.
Choke flood occurs when there is insufficient time for the liquid to dearate. Downcomer residence time preferrably should be at least 5 s, more for foaming systems. This is any easy calc. and you should be able to determine if this is your problem.
Good luck.