Pipe Flexibility Analysis are mostly developed from EPC Contractor's standard practices and Client's standard practices combined with the local regulatory requirements. Mostly it is being classified by size, temperature,connecting equipment,etc.
I think with the availability of stress analysis softwares such as Caesar II, it's much faster to do a quick modelling than doing manual calculation. But only those that fall under critical lines will be formally documented in a stress report.
But of course, I would still advice the newbies in stress analysis to know the basics and foundations of flexibility analysis (by doing some manual calculation and comparing results with software) to develop more the analytical thinking.
A good reference which I would suggest is "Matrix Analysis of Structures". From here, you will have an idea how beam element software such as Caesar was developed by automatic computation of large number of equations stored in matrices.
With the computing power nowadays, Finite Element Technology is now becoming common. But, a hand calculation to validate results is still a must.
Cheers!!!