Other answers have hinted at what I think is the crucial component, but I'm not sure it has been articulated exactly.
I play piano mostly by ear and from lead sheets (e.g., | Cmin | F7 | Bb maj | and so on). While I can read sheet music, my sight-reading is terrible. I posed this same question once to someone who was a very good sight reader and he didn't know how he did it. If, tomorrow, I decided I wanted to become outstanding at sight-reading chords, I would focus all of my energy on two things: (1) immediately recognizing the bottommost (or topmost) note in the chord, and (2) immediately recognizing the intervals in the chord. Skill (1) speaks for itself, and you can practice this by simply pointing to random staff lines and naming the note. Skill (2) is a bit more complex. The best place to start is by imagining we're in the key of C major.
For instance, when I look at Example 1, I want to instantly know that I'm playing adjacent notes in the C major scale:
And when I look at each chords shown in example 2, I want to instantly know that the notes are not right next to each other in the scale, but rather are separated by one scale tone.
Once I could identify and play any interval in C major, I would practice them all in G major, and D major, and every other key. Then I would start practicing three-note chords. Again, when practicing three-note chords, I'm still trying to cultivate my ability to see the shape of the chord and immediately recognize how many scale tones separate each note. For instance, when I look at Example 3, I'm thinking: (1) bottom note is a C; (2) second note is separated by one scale tone from the bottom note; (3) third note is separated by one scale tone from the middle note.
Ultimately, the goal is to do even less thinking than what I've described. I want to be automatic, such that I can see the shape of a chord on the page and immediately recall a particular finger/hand shape that I've practiced (e.g., for that chord I have 1 scale tone separating each finger). So I practice these until I am automatic and don't have to think at all. But I organize my practice to be systematic so that the work and learning that I do in C major supports my work and learning in G major, F# major, and all of the other keys.
Once I could recognize three-note and four-note chords, I would practice chords with sharps and flats that take me outside the scale I'm working in. Adjusting a finger up/down a half step based on the accidental is probably the third distinct skill for sight-reading chords. I tend to think that this third skill (adjusting for accidentals) would largely come naturally after doing rigorous practice on the first two. But some additional practice is probably needed.
So I think the crucial skills are (1) pairing intervals on the page to shapes of the hand, and (2) knowing where to put these shapes on the piano by recognizing the bottommost (or topmost) note in the chord.
Regarding practicing theory, I know people who are spectacular sight-readers but know nothing of the theory. And even though I might know that a chord is A7/C#, I'm not accessing this knowledge when I look at the notes on the page and try to sight-read them. Thinking about the theory would slow me down. The goal in sight-reading is to become automatic and to require no thought at all, and the only way to achieve this is through practice. Making the practice systematic can make the learning process more efficient, I think.
Regarding "looking ahead," I don't think this is something to focus on, think about, or even attempt in the beginning when at your current stage. You don't have the problem that you're dwelling too long on a chord. In other words, your problem isn't that you're reading a chord and then continuing to look at it after you've figured out what it is. If you try to look ahead to the second chord before you've successfully figured out the first chord, you'll fail and quickly become discouraged (at least, if you're anything like me!). It only makes sense to focus on "looking ahead" in the music if you already have the ability to see a chord and quickly find the correct finger/hand shape. Once you possess that skill, you can then turn to guaranteeing that you're not looking longer than necessary at any one chord.