I haven't been able to find any solid info on this, although I have read a bit about situations with "cross-flotilla" combat happening.

What I think I know so far:

• I know that, so long as you have enough ships / CP, your fleet can be split up into up to 3 flotillas, and so can the enemy's.  
• I know that at the start of the battle, each of your flotillas will face off against the corresponding enemy flotilla.  E.G. my Flotilla 1 will engage Enemy Flotilla 1, my Flotilla 2 will engage Enemy Flotilla 2, etc.

What I don't know:

• What happens when there is an unequal number of Flotillas on each side?  If I have 3 Flotillas, and the enemy only has 2 Flotillas, what determines where my "extra" Flotilla goes?  Does it just "gang up" on the closest enemy Flotilla?  Will it attempt to move into the range set for its lane on my tactics card?  Which range does it start at?
• What happens during a battle where one of the enemy Flotillas is destroyed mid-battle?  Do my Flotillas acquire a new target Flotilla and start engaging them?  If so, do they do this immediately, or wait until the start of the next full Battle Phase?  What Range will they be with the "new target" Flotilla?
• Are there any circumstances where a Flotilla may be engaging more than 1 enemy Flotilla at the same time?  Can it shoot at a Flotilla on its starboard side while simultaneously firing at a different Flotilla on its port side or in front of it?  Or do Flotillas only ever attack 1 enemy Flotilla at a time?
• Are there circumstances where a Flotilla will not engage **ANY** enemy Flotilla, despite there being available targets?  I've seen numerous complaints of players saying that one of their Flotillas will destroy its target enemy Flotilla, then just sail away into space not firing at anything, while a different enemy Flotilla continues to attack the other Flotillas.  Some people speculated that this was caused by a Flotilla not having weapons with long enough range?  However, I don't know if that is intended behavior, or possibly a bug (which may or may not have been fixed by now???)

tl;dr:

What determines which, if any, enemy Flotillas one of my Flotillas will attempt to engage during a battle?

Bonus Non-Flotilla Question:

Do Kinetic weapons' FLAK effect only protect the ship they are installed on, or can they protect other ships within the same Flotilla from missiles as well?

EDIT: Seems like Kinetic FLAK weapons can indeed protect nearby ships within the same Flotilla.

What I (think I) know... ;) The Cards have 3 lanes. They corrspond to the Lanes in the Combat window. Long Range start fighting right away (Phase 1) while any other active lanes, Medium and Short range fleets advance (often under fire) to get to their firing slots (M/S) and the M lane fleet(s) will begin fighting once they reach M range (Phase 2), and the Short move forward another level and then begin to fight (Phase 3).

Whether proper or not I like both L/M weapon types on my larger ships and rarely run many S range units. Seems best to keep everyone together for as long as possible for both coverage and support.

The biggest issue is trying to figure out how the Cards interact with one another on opposite sides. I run the odd battle "live" just to where the Fleets go based on card selection and then confirm what Card the enemy drew (It may be shown after hitting GO but whatever). It can be quite confusing at times but once you get a feel for what beats what it can be neat when you mix and Match and WIN! :)

P.S. I read somewhere that Lane 1 and 3 cannot fight each other, they are out of Range of each other thus that can cause a Draw.

Almond this is correct. The top flotilla will Almost Never Be in a situation where it can Engage The Bottom flotilla. Neighboring flotillas or adjacent flotillas will begin their targeting once the ships in the opposing flotilla on the enemy side are destroyed. Different battle cards play different trajectories and you will find sometimes a adjacent flotillas will be outside of their fireing arc to engage as well. Broadsides are limited to seventy degrees and turrets are 270 degrees if I am not mistaken.

Also all cross flotilla firing will start at long range generally, the only case this does not happen if both opponents pick short range cards, then the cross flottillas may begin at medium range.

There is not much documentation on this but I hope this helps.