Your question, as far as I know, has not a direct and official answer..but I think we can put together some information to achieve a good answer anyway (or at least try to achieve it).
First: keep in mind that combat flexibility states that you gain a feat (or more as you level up) only until your next daily preparation.
Combat Flexibility: [..] When you make your daily preparations, you gain one fighter feat of 8th level or lower that you don’t already have. You can use that feat until your next daily preparations.
This means that every day you lose and gain a feat so we can be pretty sure that combat flexibility gives you temporary feats and this temporary feats are not intented to give you anything else other than the possibility to use for ~1 day the feat you have chosen. Keep also in mind that probably Paizo would have written an information like the one you are searching and this kind of games are plenty of phrases like "this feat count as a prerequisite to other feats" (improved flexibility has that magic phrase for example and specifies that count only towards other feats that you gain with this abilities).
Second: this is what the rulebook states about prerequisites...and yes, you can bend this rule a bit to do what you are asking I think.
Prerequisites: Any minimum ability scores, feats, proficiency ranks, or other prerequisites you must have before you can access this rule element are listed here. Feats also have a level prerequisite, which appears above
In conclusion, my suggestion is (at least for now) to play using only what is written down in the books and follow the rule: "if it's not written...it doesn't work". (And at my table I'll not allow something like that probably)
Edit: After a little more research i found this line of rule inside the retraining part of the rulebook
If you cease to meet the prerequisites for an ability due to retraining, you can’t use that ability.
Hope it helps!