No.
Character Advancement
When adding new levels of an existing class or adding levels of a new
class (see Multiclassing, below), make sure to take the following
steps in order. First, select your new class level. You must be able
to qualify for this level before any of the following adjustments are
made. Second, apply any ability score increases due to gaining a
level. Third, integrate all of the level's class abilities and then
roll for additional hit points. Finally, add new skills and feats.
The order of how you level matters. You're allowed take a feat the same level you gain the prerequisites only because gaining feats is the last thing you do. If the prerequisite is a skill, spell, or ability, you already have it by the time you take the feat.
Of course, if the prerequisite is another feat, you must already have the prerequisite feat before you can take the desired feat. However, since character advancement is an ordered process, if you gain multiple feats in a level1, you can choose to take the prerequisite feat first. You can now take the desired feat.
In your example, you can take neither feat first since neither feat has its prerequisite met.
1 Class abilities that give bonus feats give them at the time you normally add new feats (after skill points). It's unclear if you choose your standard feat before your bonus feat or vice versa, but I would generally allow players to select feats in any order if it matters.
The DMG rules are consistent if you count the exact number of spaces, while measuring either way around.
In other words, if you have two creatures adjacent to a middle creature, then count both clockwise and counterclockwise. If the number of spaces (in either direction) equals the number you're trying to count, then there are that many spaces in between.
The trouble here is a geometric property that on a hex grid, Large and Gargantuan creatures are surrounded by an odd number of hexes. If you pick two of these hexes (as possible flanking locations), and count the spaces in between, then you are guaranteed to get different measurements clockwise versus counterclockwise.
However, it is possible to pick two surrounding hexes such that, if you count the in-between spaces both clockwise and counterclockwise, the measurements differ by 1. This is the closest way to split the difference (an odd number), so the DMG uses these measurements to determine flanking. Thus if a creature is surrounded by an odd number of hexes (i.e., they are Large or Gargantuan), then an adjacent attacker can flank with up to two other adjacent attackers.
When two Medium creatures are adjacent to a Gargantuan creature, there are 13 free adjacent spaces. If you can count 6 one way, then you must count 7 the other way. In this case, you counted the short way, but you still counted exactly 6, so they are flanking.
When two Medium creatures are adjacent to a Large creature, there are 7 free adjacent spaces. If you can count 4 one way, then you must count 3 the other way. In this case, you counted the long way, but you still counted exactly 4, so they are flanking.
By comparison, with Medium and Huge creatures, they are surrounded by an even number of hexes. It is possible to pick two of these hexes, such that you can count the same number of spaces in between both clockwise and counterclockwise; these are visibly the flanking positions.
As a side note, the second DMG quote only applies to a square grid. Otherwise you are dealing with creatures that don't have "opposite sides or corners".
So for the purpose of determining whether two attackers flank a Large (or Gargantuan) creature, you will have to count either clockwise or counterclockwise.
In the above examples, there are exactly 4 spaces counted in between the attacking creatures.
Best Answer
Let's start off with some names. We have Derek the Darkstalker, Bob the Beholder, and Nancy the non-Darkstalker. It's the middle of combat, and the map currently looks like this:
At this point, neither Derek nor Nancy are flanking Bob. It's Nancy's initiative, however, so she takes a free 5 foot step to her left:
Now, both Derek and Nancy could flank, according to the rule on flanking. However, it's still Nancy's turn, so she is designated as the flanker, Derek is the assistant, and Bob's the potential victim.
Rules are always evaluated from most specific to least specific, through a process I refer to as "targeting," and what is specifically referred to as "specific beats general." In other words, a rule that targets another rule is more specific than the rule or rules it targets, and will apply first. I've included the relevant text and links below.
Flanking targets any creature in the correct formation, all-around vision targets flankers, and Darkstalker targets all-around vision. For each attack, we determine which rules apply from least specific to most specific, then resolve them in reverse order.
So, since it's still Nancy's turn, she decides to attack. First, we know that they are in flanking position. Second, we also know that the beholder's vision is an exception to flanking. Since there's a conflict in the rules, we depend on Specific Beats General (SBG) to determine which rule applies in this case. The most general rule is obviously the flanking rule. The all-around vision rule is a specific exception to the flanking rule, thus negating the bonus. Nancy is not flanking. Notice how the general rule was observed first, followed by the specific rule, which was observed second, but applied first, negating the flanking rule.
Next, it's Derek's turn. We're already set up for flanking, so Derek decides to attack. Now, thanks to the Darkstalker feat, we have three rules in play, with multiple contradictions. Again, we turn to SBG to determine which one is correct. First, we know that Derek has an assistant, Nancy, who is threatening Bob, so Derek is flanking. Second, we know that Bob cannot be flanked. Third, we know that Darkstalkers specifically target creatures like Bob.
There's only one logical order that we can apply these rules, so we stack them up: flanking, all-around vision, Darkstalker. We know that this must be true because if all-around vision was more specific than Darkstalker, the feat would literally be useless, because any all-around vision creature would trump the feat that was designed to defeat all-around vision. In this way, we can think of conflict resolution as a last in, first out (LIFO) stack. The Darkstalker ability wipes out the all-around vision ability in this conflict, leaving the flanking ability to apply its +2 bonus.
Note: The rules don't call out a LIFO stack specifically. It's heavily implied by the way the rules are written, and it's the only way a DM can consistently come up with results for any combination of rules. Most questions of this nature usually end up with multiple interpretations because the interpreter cannot come up with the order of specificity.
Observing the conflict as a LIFO, it makes it easier to see the results. Different DMs may decide to do it in their head, call a friend, choose what they think should happen, etc.
Summary: The Darkstalker is flanking on their turn if they have an assistant 180 degrees opposite the target that is capable of attacking, even if the target has all-around vision. Note that there are other types of flanking negation that this feat does not negate. It only works on a specific type of creature in a specific situation.
From the Player's Basic Rules:
From the SRD: