Using the word "conceded"?

That doesn’t sound right. To concede means to give in or to accept a compromise or to accept an opposing argument.

Depends on what you want to say:
Concur
Consent
Assent
Acquiesce
Accede
Permit
Allow

These are all options. From what you said, you might be better off with “She had initially concurred, but…” or “She had reluctantly consented…” or “She had acquiesced, grudgingly…” or “She had allowed the design to go through, but…”

You can say something like:

’ “I guess we could make do with that,” she conceded.’ BUT

If she actually conceded, it would be making ‘a concession’.

No.

concurred with
approved of
consented to
assented to

You’d use “conceded” like this:

She had criticized the design mercilessly, but after he insisted on its superiority over her favorite, she conceded the point.

or

I thought she’d never agree to let me go, but after I promised her I’d behave myself, she conceded.

Think of it as “gave in.”

For the sake of your story, though, you might want to ask yourself why you need to say the same thing several times. Perhaps there’s another take that would call for only one “agreed.”

“she conceded that the design was flawed” I think works better

Only if she is admitting that it’s flawed. I think the intent is that she had agreed to it even though it was flawed, and the questioner just wants several different ways of saying she agreed to it.

“With” isn’t usually used with conced, so “She had conceded to the flawed design” is better, but adds meaning to “agreed with”. To concede means to give in, rather than to simply agree.

She was so conceded that she thought that song was about her.

@ratboy I assume you mean conceited and not conceded.

I think shilolo’s “reluctantly” above actually helps you put your message across a lot easier than “conceded” or any of its synonyms. If you don’t want to say “reluctantly agreed” or “reluctantly consented” you could say “reluctantly accepted” or paraphrase the whole thing using something like “finally gave in” or “despite her initial objections…” etc.

Need to know: did she protest the design? Did she mention the flaws? Was it a big issue? It also helps to know WHY she did what she did.

You don’t “agree” with a design. You can agree with a design choice, ex., “She agreed with the selection even though she knew the design was flawed”.

How about, “the flawed design, she being ignorant to the concept…”

When in doubt, @Jeruba comes to the rescue. She is the superhero of grammar and language in general.

Anybody know if Jeruba wears a cape? She might be able to pull off that look.