Can the feat a Fighter gains from Combat Flexibility satisfy the prerequisites for other feats you gain at level-up?
For example, Quick Shield Block requires Reactive Shield. If your Combat Flexibility feat is Reactive Shield, can you take Quick Shield Block during your level-up, then change your Combat Flexibility feat to something else the next day?
Combat Flexability explicitly grants you a feat (Core Rules, pg. 143):
When you make your daily preperations, you gain one fighter feat of 8th level or lower ...
If you use Combat Flexability to gain Reactive Shield, then for all purposes you have that feat.
The sticking point comes from how feat prerequisites work. The definition of prerequisites is found on page 18:
Any minimum ability scores, feats, proficiency ranks, or other prerequisites you must have before you can access this rule element are listed here.
A prerequisite isn't only required at the time you select a feat; it's required anytime you want to "access" that feat. In your example, you wouldn't be able to utilize Quick Shield Block even though you have it, because you no longer meet the prerequisites.
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!
Unlike in Pathfinder 1e, you need prerequisites only to take a feat, not also to benefit from having it. Similarly, however, you can use abilities gained from any source to meet prerequisites. That means that as long as you have the feat gained from Combat Flexibility continuously during level-up (which you certainly can, since you can skip daily preparations and the feat lasts until your next one), you can use it to qualify for feats you otherwise would not qualify for and then change it to something more useful the next day.
