My understanding of the engine flush process appears to differ from everyone else that has commented or answered so below is my take on it.
An engine flush (engine oil or transmission oil) is the process in which ALL of the oil is drained from the system and re-filled; this does not necessarily mean that additives are added to break down sludge and inadvertently cause issues with seal.
For instance my car has 12 quarts of transmission fluid. If I simply drain it from the bottom I only get 3 quarts so I only have to fill 3 quarts.
If an engine flush is performed then they need to put back in the exact same amount of oil which they took out. So if they truly flushed 12 quarts via an oil vacuum then they need to put back 12 as well. In this lies the problem.
When filling the transmission with oil they might not reach all of the places where they took it from. There are a LOT of nooks and crannies which might not get lubricated unless you knew to specifically target those areas.
If a nook or cranny is left unfilled then YES, you can absolutely experience a blown transmission.
This same principle applies to engines, brake lines, and cooling systems.