I am aware of two varieties of "safe" plastic flips which fold to 51 mm (2 inches) on a side. Abafil cases have 48 mm squares and 50 mm is a bit too big. They would fit at most a 48 mm flip. Are there 48 or 47 mm "safe" flips?
Valen i purchased a 1000 safe flips from a manufacturer in NJ. they are 50mm but maybe they could make you some to fit your 48mm space. FAC frame a coin, Madison, NJ. i Google them, they carry the 1.5 and 2 also 2.5 in.maybe they can custom order you some 48mm, hope this helps.
Abfil makes 2 3/8" space 15 per tray for the purpose. Waddell sells them for $55. I believe if coins are going to be in a flip, it might be an option to buy cheaper brand trays that fit the cases.