Applying anagrams to flexagons appears to be quite a challenge. Combining the rearrangement of letters in words or phrases, using each letter only once, plus, allowing for flexing operations may be stretching the trihexaflexagon's capabilities. Here's where it may be time to send for the computer cavalry. I figure that at a minimum, for starters, there must be some way to apply at least one of these following anagrams:

ladies/ideals, Hamlet/Thelma, action/atonic, actors/costar, diaper/Idrape, detour/routed, fatima/Iamfat, mirage/imager, molars/morsal, onehug/enough, orator/toroar, rescue/secure, resort/orrest, seance/ascene, shadow/howsad, simian/isiman, asiren/isnare, subtly/butsly, tennis/innets, united/induet, and violet/loveit. Anyway, you can see that there should be a good chance of more material appearing here. I wager that someone will find something to contribute long before I can.