No, we would not say this. The word 'quite' is wrong in this sentence.
(Ellen Hogue is right that there is a difference between American and British English with how 'quite' is used as a modifier. However, this really only applies in the affirmative. For example, it is normal in BrE to say "I quite liked flowers" to mean that you liked them in a 'lukewarm' kind of way).
'Quite' does not work in this way in the negative. In general, it makes no sense to add a negative to 'quite' : you either liked them, you didn't like them, or you 'quite liked them' - 'never quite liked' is just odd.
In some cases, it is possible to put [never/not] 'quite' before a few verbs, but the meaning is slightly different. For example:
"When I was a child, I spent a lot of time with my great-grandfather. He spoke an old-fashioned dialect and I never quite understood what he was saying."
This means 'I never totally understood what he was saying". '[Not/never] quite' means 'not 100%'. For example, if you said "I'm not ready yet. I haven't quite finished my lunch", it means that you haven't completely finished your lunch. As you can see, we use this to express quantitative ( rather than qualitative) ideas.
The most normal way of expressing the idea which (I think) you mean is this:
"I never really liked flowers"
or
"I never liked flowers very much".
If those don't work for you, why don't you just tell us what you want to say in Spanish? There are plenty of people here who could give you an exact translation.