When learning compounds, e.g., koutei 肯定 "affirmation" do you mainly drill yourself in order to master the spoken form first, i.e., [imagine person repeating the following over and over]:

"koutei - affirmation"
"koutei - affirmation"
"koutei - affirmation"

and then study the kanji?

Or the other way around? Or sort of both at once?

I was trying to do both at once (kanji plus pronunciation) but found that in many cases I could remember the meaning from the kanji but couldn't recall how to say the compound out loud, so I switched around and am focussing on learning the pronunciations first then the kanji.

How do others approach this?

Both. Meaning always sticks faster regardless since you can build mnemonic for hard to remember words or add extra sentences using the same word. Getting the reading to stick is sometimes hard and there is no problem with that. Its expected that some words might take 60+ reps before you finally remember it, while others only take 10-20. I'd also add/move up other words that used parts of the compound to aid in learning.

I find jukugo very difficult to remember without the kanji.
Kanji plus pronunciation does trip you up when you start learning a word, but it gets easier after a while (one week of Anki-style reviews - I know you don't use Anki, though.) Despite the fact that I don't really study individual readings at all (because it takes far too long and you might as well pick them up from actual words), it actually is much easier to remember words when you already know how to read the kanji individually (but you're a pretty advanced learner so I guess you probably must already know at least one reading for every kanji in RTK?)

Btw, I never had any trouble remembering words back when I was learning by rote using Basic Kanji Book: I read the entry for each kanji, filled the grids, did the exercices and then dumped all the vocabulary into Anki and I usually could get it right right away.

Both, kinda.
Because you might already know 定着, you can guess that 定 will be pronounced the same in both; if it turned out that it isn't, then you'd want to remember that.

Basically, at the beginning, I was doing a lot of work on reviews to learn to recognize jukugo and be able to read them. After enough kanji reading schemes got soaked up, it became a lot easier to guess the reading, which made reviewing reading and meaning at the same time much easier.

I agree with poblequadrat, it's a lot easier to remember compounds with kanji. Maybe not at an absolute beginner stage, but you're much further than that, so I suggest using kanji.

Since you say your problem is the reading, why not focus on the reading primarily instead of the meaning (not actually changing anything, just telling yourself that, if you can't remember the reading, then you're wrong)? This way, you might get better at remembering readings when introduced to new jukugo. Learning words based on their pronunciation first means that you have to completely relearn the word in its written form.

When adding words to Anki, I always create 2 cards, one with the kana word and one with the kanji word (this is automatic from the way I set up my cards; I can even create a 3rd card for an alternate kanji spelling if I want/need it.).

Then I drill the kana word first and schedule the kanji word to start some days later.

For words I learn in context and never drill on, well, those tend to be words that are pronounced exactly as I'd expect based on their kanji spelling. I guess you could say I learn meaning and pronunciation simultaneously but I don't know if that's true when the pronunciation is obvious. Or easily learned. 紫煙 is one I learned from context recently. After looking it up once I realized that 紫 has a thread bottom radical, which is a clear phonetic signal for a し pronunciation and I already knew けむり＝えん, so job done. Just have to remember that the Japanese think cigarette smoke is purple and no problem!

It depends, if I'm working with a subtitle or a transcript I'll highlight the word in question in blue and write it in hiragana, while the rest of the sentence will be just be Ctrl+C'ed. I add both words that are new to me and ones that I didn't understand when hearing, but would have if I had seen the kanji. If I'm reading and the word in question strikes me as something that I probably just will see in writing I'll use the kanji form.