I think he's potentially a little taller than his "official" height... either his record is out of date or others are, maybe both.
Heights of this group from left to right, according to the Premier League website, I've converted roughly into feet:
Kane - 1.88m (6'2")
Rashford - 1.80m (5'11")
Shaw - 1.85m (6'1")
Saka - 1.78m (5'10")
Sancho - 1.80m (5'11")
Sterling - 1.70m (5'7")
Grealish - 1.75m (5'9")
Stones - 1.88m (6'2")
Phillips - 1.78m (5'10")
I'd say from that group, the only players who are significantly taller (as in, you can tell by eye without measuring them and be confident it's not an issue of perspective or posture) than Jack are Kane, Rashford and Stones.
Jack's clearly significantly taller than Sterling, and looks to be taller than Phillips too as long as we're not measuring Phillips' hair.
It looks like Jack's roughly the same height as Shaw, Saka and Sancho - but the problem is there's 10cm between the official heights of these four players, with Jack as the shortest.
But look, Jack and Luke together:
Jack and Bukayo together:
And Jack and Jadon together:
Sancho and Saka's official heights may be accurate, but if so, Grealish is definitely taller than 1.75m and Shaw is definitely shorter than 1.85m (also, there's absolutely no way Shaw's taller than Rashford... I think we could probably swap their official heights and it'd be more accurate).
Bonus evidence because I love this picture. Foden's official height is 1.71m, which seems about right as in pictures with Sterling they look a very similar height. There is absolutely no way that the Foden/Grealish height difference is only 4cm. Jack looks closer in height to Stones - who's officially 13cm taller than him - than Foden looks to Jack.
And of course, I let slip I have bipolar disorder and then my next action is 8am footballer height analysis.