No there are no missing sharps of flats.
The C major scale is used as a template for any scale. Its a good template because it is easy to write out. You can use the Am scale for the minor chord template.
So for the chords in the key of D you make the table starting with the D chromatic scale and the D major scale in the first line. Then you find the 3rd, 5th and 7th. You may not need the chromatic scale, but it shows you how the scale works without trying to remember a formula.
Once you get the hang of it you can also write in the chord names under the columns. Its called the diatonic sequence.
The 3rd, 5th and 7th rows are actually modes of the major scale. You can find the greek names if you are bored, or just remember them as 3rd, 5th and 7th mode things. You only need to know the right technical names if you are going teach a class. When you are working out the chords on the fretboards, you don't need any extra info to distract you.
Once you get the hang of it, the more complicated chords will not be hard to work out with just your fretboard and your brain.
The on-line apps are nice and easy. But they wont show you arpeggio patterns for example. When you are fingerpicking or playing chord fragments, you don't need to make a whole chord shape, you can use what ever is in reach to make the chord or chord fragment.