Well, for "Average" difficulty the book actually recommends PC starship tier minus 2... rating the enemies for tier 16 instead of tier 14 in this case would constitute a boss battle. Now, I haven't run encounters at that level / with that many ships yet, so I don't know from experience yet if a tier 16 encounter made of 6 ships actually would be as hard as a single tier 16 ship, I'm going exclusively off what the book says... but it seems reasonable just because of action economy, even if their attack bonus etc is lower they get far more attacks per round so more chances to actually land lucky hits.
ANYWAY. As I read it, to make a tier 16 encounter out of 6 ships as you requested, I believe each ship would have to be tier 11. A trio of tier 11 ships equates to tier 14 per the book, then if you treat each of those "wings" effectively as one enemy, then two of those tier 14 wings would rise to tier 16. My gut says it would actually be tier 15 in practice, though, just like you can throw literally 100+ CR 1 monsters at a level 16 party and it still won't be a level 16 encounter in all but the most unusual circumstances where the monsters have terrain advantage or other things in their favor. So going off that intuition, I'd guess tier 12 ships for your target tier 16 encounter.
Per CRB P.326, the CR of multiple same-tier ships in an encounter is based on treating groups of ships as individual ships of a higher tier. A pair of ships both at tier X is treated as a single ship at tier X+2; a trio of such ships treated as a single ship of tier X+3. This happens twice for six ships of tier X. First to combine trios into a pair of two virtual tier X+3 ships, and then to combine that pair into a single virtual tier X+3+2 (tier X+5) ship.
Since the CR of six same-tier ships is calculated as if they were a single tier+5 ship, the actual tier of the ships in an encounter of any given CR will be CR - 5. CR 16, which is nominally a "hard" encounter for APL 16, would thus have tier 11 fighters. CR 14, which is nominally an "average" encounter for your party, thus has tier 9 fighters.
Fuzzypaws covered that, but I thought that having that explicitly broken down a bit more might help since this is giving you some trouble.
As for your second scenario with the tier 14 "battleship" and tier 6 fighters, the same section provides the rules.
...use the highest-tier ship's tier as a base and add 1 to this value for each additional starship within at least 2 tiers of that starship. If none are within 2 tiers, add up the tiers of all the additional starships and add 1 to the base value if the total is [sic] equals or exceeds the base starship's tier. Use this modified value when determining the encounter's difficulty.
This paragraph is presented as being about PC fleets, but the very next one says to refer to it when dealing with non-matching NPC ships too.
So you have a tier 14 battleship that provides the base. Tier 6 isn't within two tiers, so you take the sum of the fighters (6*6), and since 36 is greater than 14, you add 1 to the virtual tier of the encounter. With no other modifiers, a tier 14 capital ship with 6 accompanying tier 6 fighters is thus CR 15, which is nominally a "challenging" encounter. If you wanted the CR rating to be higher or lower, this is most easily adjusted by changing the tier of the battleship.
Pragmatically speaking, I don't expect even six fighters 10 tiers lower than the PCs to be a significant factor, but the nature of starship progression may make them more threatening than I give them credit for depending on how your players' ship is built.