Fate Worlds: Kriegszeppelin Valkyrie

You might find what you want in Fate Worlds Vol.1, specifically "Kriegszeppelin Valkyrie" (KV). It is a mod/campaign where PCs are WWI pilots. Their planes are stationed on a giant flying aircraft carrier, the eponym Kriegszeppelin Valkyrie. Change "planes" to fighters and "flying aircraft carrier" to "capital ship", and you have a good start!

Now, that's probably not enough detail for you, so let's mention some rule points and how they might fit what you would like to do. I will avoid quoting extensively considering the book is not open source, but here it is.

Fighters

Fighters are represented by Stunts. Each fighter costs a given amount of Refresh (between 0 and 3) and gives specific bonuses. One fighter would for example cost 2 Refresh and grant a +2 to Pilot rolls to defend and create an advantage due to high maneuvrability. Another would cost 1 Refresh and grant Weapon: 2 once per combat due to heavy guns.

As for damage, the combination Pilot+Fighter symply uses the pilot's stress tracks as is. You could however create a separate "Piloting stress track", with additional stress boxes for higher Pilot skills.

Dogfights

Dogfights in "Kriegszeppelin Valkyrie" are handled through a simple rule. Fighters making a straight attack without first placing an advantage on their target can do no more than one stress damage, no matter their Stunts, their roll, their final result, and so on. A fighter needs to first succesfully create an advantage on their target to be able to do full damage.

Capital ships

The Valkyrie in "Kriegszeppelin Valkyrie" is treated as its own character. It has its own stress track, Aspects, Trouble, Stunts, and skills. It uses its captain's skills and stress tracks for mental attacks.

This makes sense, considering a ship with a huge crew is less dependent on its pilot's skill. Put Han Solo at the helm of a capital ship, and it probably won't be much nimbler despite his superior skills.

Other ships

"Kriegszeppelin Valkyrie" has a couple of other ships described as opponents:

• Gunship: Heavy guns and bombs
• Troopship: Transport carrier
• AA Gun: Anti-aircraft gun
• Airship: A big flying ship, but smaller than the Valkyrie.

Fate System Toolkit: Scale

You mentioned it already, but for the sake of completeness I would like to point out the Scale subsystem in the Toolkit which might help you reach what you want.

You define a number of scale steps (3 or 4). Larger entities have a number of bonuses against smaller ones. This allows you to split ships into size categories (fighters, freighters, small capital ships, big capital ships). The more categories you have, the more difficult it becomes for small ships to affect bigger ships, which might or might not fit what you have in mind.

You could change the bonuses to be more similar to Star Wars RCR: for every step separating two ships, the smaller one has bonuses to attack and defense, but the larger one has bonuses to damage and armor.

It seems to me that your question is two fold. I may be wrong but you seem to be looking not only for a technical point of view but also from a role-play point of you.

The technical aspect is quite easy to answer:

You will need two items to produce your concoctions(extracts, mutagens and bombs):

Kit, Alchemy Crafting

Price 25 gp; Weight 5 lbs.

An alchemist with an alchemy crafting kit is assumed to have all the material components needed for his extracts, mutagens, and bombs, except for those components that have a specific cost. An alchemy crafting kit provides no bonuses on Craft (alchemy) checks. (This item was previously called an “alchemist's kit”, and was renamed to avoid confusion with the set of adventuring gear called an “alchemist's kit.”)

The second item is your

Formula Book

An alchemist may know any number of formulae. He stores his formulae in a special tome called a formula book. He must refer to this book whenever he prepares an extract but not when he consumes it. An alchemist begins play with two 1st-level formulae of his choice, plus a number of additional forumlae equal to his Intelligence modifier. At each new alchemist level, he gains one new formula of any level that he can create. An alchemist can also add formulae to his book just like a wizard adds spells to his spellbook, using the same costs, pages, and time requirements. An alchemist can study a wizard's spellbook to learn any formula that is equivalent to a spell the spellbook contains. A wizard, however, cannot learn spells from a formula book. An alchemist does not need to decipher arcane writings before copying them.

Extract's preparation How to make an extract. Most of the text around extract can be reduced to the funny (or not) "spell in a bottle".

In many ways, they behave like spells in potion form [...] An extract, once created, remains potent for 1 day before becoming inert, so an alchemist must re-prepare his extracts every day. Mixing an extract takes 1 minute of work—most alchemists prepare many extracts at the start of the day or just before going on an adventure, but it's not uncommon for an alchemist to keep some (or even all) of his daily extract slots open so that he can prepare extracts in the field as needed.

Alchemist extract are like spell really but with a kick they don't take as long to prepare, unless you have more than 60 extracts and at this point well... breaking action economy should not be too hard. The downside is that you need to redo it every day so no storing for long winter nights!

Mutagen's preparation

Now comes the preparation aspect on how to make Mutagens. As far as I can tell, the usual in D&d is to be quite abstract and left to the imagination of the player the details. Most of the time for spell caster you have to go into splat book and descriptions to get a "look and feel" and not only the "use a standard action".

Mutagen (Su)

At 1st level, an alchemist discovers how to create a mutagen that he can imbibe in order to heighten his physical prowess at the cost of his personality. It takes 1 hour to brew a dose of mutagen, and once brewed, it remains potent until used. An alchemist can only maintain one dose of mutagen at a time—if he brews a second dose, any existing mutagen becomes inert. As with an extract or bomb, a mutagen that is not in an alchemist's possession becomes inert until an alchemist picks it up again.

Emphasize mine... A mutagen is brewed, so it is likely to be prepared like a potion or extract but being far more potent it takes a whole hour to make one dose and the alchemist aura can only "power up" one at a time.

From the Alchemy crafting Kit, we know that you have all you need is in it.

So you now have the physical elements and you know that it takes you an hour to brew it.

I hope this will be sufficient for you to feel comfortable using your mutagen.