That's a good one.
So I'm writing a flashback scene and my question is, does the whole flashback need to stay in past tense? Writing "he thought" and "they did" over and over becomes messy.
First of all, you did write your story in past tense (= imperfect), as I saw in the other thread. Therefore a flashback will be in past perfect.
The copious use of "had" feels awkward, [...]
It is indeed tedious to use past perfect during a longer passage. A certain "royal" horror author, whom I can recommend when it comes to stylistic originality, tends to write shorter flashbacks like that (longer ones are mostly put into an own chapter): The first few sentences are in past perfect, and when the flashback scene is established, he switches to imperfect.
Another possibility is to give the scene its own sub-chapter or, as you call it, cinematic style:
Kareem took a deep breath and looked up to the moon, it had been a long time since he had prayed to Lahilah, the southern goddess of the moon and illusion, her impassive face now shone down upon him. No, it was different this time, he had used her moonlight for much evil before, now he would use it for good. (nothing new till here...) He would use it to find her...
From now on you can write the flashback scene like a normal part of the story. Please notice that some verbs are still in past perfect, for the actions they are describing take place earlier than the actions in the actual flashback -- which, I reckon, is the conversation with Nina.
It hadn’t been difficult to locate the pleasure den, Firendil’s accurate landmarks had helped, away from the sea on a hill guarded by the Red Chain.
He had had to ask only two trusted merchants [...]
Kareem gulped and concentrated on his coffee somewhere in the back of his mind he knew what would happen tonight.
Nina’s eyes narrowed.
[...]
I take this as a non-flashback sentence:
The tall southerner took another deep breath calming himself , he would find her and save her for Firendil. His conversation with Nina earlier still bothered him, he prayed to Anaret there was another way.
If it is, you better remove it from the scene, or it may confuse the reader. If you want to keep it, put it between, e.g., 2x3 blank lines to make it stand out. Instead or in addition you can use italic (my italics above are just indicating quotations or comments):
He had had to ask only two trusted merchants to receive the same dreamy lustful gaze, word of the moon skinned, fat titted, elven pleasure slave was quickly spreading through the upper merchants. Both of them had chuckled and suggested Kareem bring his gold pouch, even for an hour her owner demanded a sultan’s tribute.
The tall southerner took another deep breath calming himself , he would find her and save her for Firendil. His conversation with Nina earlier still bothered him, he prayed to Anaret there was another way.
“So big guy, you know where the pleasure den is, what now?”