During the season 4 finale episode, we saw Devoe using several meta-human abilities like gravity, duplication, telekinesis etc., but why didn't he use the luck ability against Barry (during his escape from Devoe's mind).
Or am I missing some plot here?
I don't remember if there's an explanation in the show, but I can hazard a guess.
During the episode where we're introduced to Hazard, we see that her luck ability is very passive. Things just go her way to the point where she can casually walk in to a bank and walk out with money without any interference. So it's not something that Devoe can turn off or on. It just is.
Her power also seem to be limited based on what is physically possible. All the good and bad things that happen are possible albeit extremely unlikely (hence lucky). The more her power grows, the more highly unlikely, but still possible events occur that give her good luck while giving everyone else bad luck.
We see this later in the episode with the Casino scene. (Very) Bad luck befalls everyone around her while good luck hits her. All the good and bad luck is still within the realm of possibility. In this case, even more unlikely, but still possible scenarios play out because her powers have amplified as she used them.
So her powers are limited to what is possible. Her weakness would be to put her in a place where nothing good can possibly happen by chance. Enter Devoe's mind which seemed to be based primarily on his memories. Those memories can't be altered, so there is no chance that anything can happen to Barry beyond slight deviations. So he didn't use them simply because they didn't work in his mind.
Because he didn't think it would be necessary. Devoe makes a show of pointing out that they are in his mind, and that he can control the whole environment in there.
If he's in complete control, there's no reason for him to need to rely on the power of luck, so he just doesn't use it. Doesn't work out so well for him in the end though.
The luck power is explained as being able to affect quantum fields of probability, and therefore to manipulate chance. Devoe is a major control freak and believes he has considered all possibilities - nothing has been left to chance. In his own mind, there IS no chance occurrence possible.
According to me, Devoe didn't use luck when Flash was in his mind because when he takes the ability of a Meta, the source of the ability could have been stored in his brain but not in the subconscious part of the brain. Therefore he can use his abilities only physically not mentally.
