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In the blues scale, when I form the diatonic chords of this scale is the blue note (D# in the case of C major blues) also taken into account when forming the chords?
so in C major blues scale: C D D# E G A the chords would be:


1. C D# G

2. D E A

3. D# G C

4. E A D

5. G C D#

6. A D E

Or do I just form diatonic chords of the underlying pentatonic scale? Also, not too sure how I'd form the diatonic chords of the pentatonic scale.
C major pentatonic: C D E G A, the chords would be:


1. C E A

2. D G C

3. E A C

4. G C E

5. A D G

Does this look right?

You could make chords out of blue notes, but why would you?

In general the blues scale(s) is only applied in certain circumstances: unsurprisingly, in blues music. The best answer to this kind of question, in my opinion, is to observe blues music to determine blues' chords.

You certainly could write blues music with chords like the ones you listed above, because no one's stopping, you, but when I think of "blues chords", I think of three chords, and only three: The I7, the IV7, and the V7.

I think that blues chords aren't really directly related to the blues scales or the pentatonic scales in general; they just seem to be the I, IV, and V with their dominant 7ths on them (and sometimes, to spice things up, the ♯9). The real beauty of the blues scale is its melodic capabilities, not its chord construction. The blues chords are a framework around which the blues scale is used melodically; while most of the notes in the blues chords have at least some justification in some blues scale, the real reason those chords exist is because they carry a "blues feel", whether that be due to societal influence of not.

Take the major blues scale C-D-D♯-E-G-A. The chords that traditionally go with this scale are C7 (C E G B♭), F7 (F A C E♭), and G7 (G B D F). The note F appears multiple times, and yet is never mentioned in the major blues scale that's being played. The note B♭ is part of the tonic chord, and never appears in the blues scale. Another way of thinking about it is that one can apply the blues scale of the chord being played to the melody as well; when playing F7, (F-G-G♯-A-C-D) all work pretty well in the melody, providing more justification. But in my opinion, the justification isn't important, because the chords weren't actually from the blues scale at all.

The blues scale is a loose association of notes that when used melodically tend to be perceived as "bluesy". The blues chords tend to use similar groups of notes, but there's no useful direct relationship between the blues scale and blues chords.

It's the same thing with the pentatonic scales. At least in popular music (because it's different in more ethnic-sounding music), the pentatonic scales aren't the only allowable notes. Plenty of pop songs use just the pentatonic scale in the melody, but the chords are far from restricted to that scale. Usually, it's I-IV-V and sometimes vi, quite similar to the blues in terms of framework around which the melody is implemented. The whole point of the pentatonic scale is to remove the notes with the most tension (well, that's at least an important effect of using the scale), but without any tension, all of western harmony falls apart. See the duality?

That said, the pentatonic scales make some cool chords. And of course, not all blues songs only use three chords, and not all pop songs only use "the" four chords. However, the scale of the melody and the scale of the chord do not have to be the same, and often they arent in those two styles/harmonic environments.

TL;DR: Blues scales don't affect the blues chords. Same for Pentatonic as used in western music.

The so-called blues scale isn't really a thing. Jazz, blues, and rock and roll music doesn't really build melodies out of such a scale. The blues scale is sort of a crutch that teachers use to help students get started with playing the blues, and different teachers don't even agree on what notes are in the scale. The form you give, C D D# E G A in C, isn't even one that I've ever seen before. If someone held a gun to my head and demanded that I name the notes in a C blues scale, I'd probably say something like C Eb F F# G Bb. But you can throw the D or the A in, or not use the F#, or play E instead of or in addition to Eb.

You seem to be taking a certain version of the blues scale and building chords by starting on a certain note and playing every other note in the scale. This does work in the sense that if you start from a diatonic scale and do this, you get the usual triads and seventh chords, but it's not really where harmony comes from or how chords are constructed. At the physical/physiological level, the major triad clearly comes from the overtone series, but in general chords are just combinations of notes that occur in music. Originally they occurred because people were writing music with 3 or 4 voices, and combinations of notes came about because of the way the different melodic lines interacted.

There are lots of ways of making various scale patterns fit with various chords in a bluesy context. It would be boring and static if the only way of doing it was to make the chord and melody out of the same set of 5 or 6 notes. Some examples:

You can play a chord consisting of C E G Bb Eb (usually voiced with Eb on the top). Or a piano player can play a C7 chord (C E G Bb) while the melody line can be Eb.

Any note whatsoever can be played as a chromatic passing tone. For instance, over a C7 chord you could play Bb B A, and depending on how you executed it and fit it into the musical context, it could sound fine.

In a 12-bar blues in C, if you're improvising melodically, then it tends to sound boring and static if you never recognize the changes in harmony with changes in the notes you're using in the melody. If you play Eb over the F7 chord and then play E over the C7 chord, it gives the listener the feeling that you're helping to tell the harmonic story. If you play E over the F7 chord, it's probably going to sound just plain wrong.

Scale fragments can be transposed. For instance, you could start a 12-bar blues in C by playing a lick on the notes G A Bb over the C7 chord. Then when the chord changes to F7, you can transpose the same lick to C D Eb, and similarly, if you like, for the rest of the chord changes.