Disclaimer: I have never eaten a graham cracker.
Based on this recipe for Graham Crackers, a "graham cracker taste" would essentially be a wholemeal biscuit/cookie flavour, with a brown-sugar accent.
To get the toasty/bready flavours, I would use a base of 5% biscuit malt and 5% crystal to compliment a good base-malt like Maris Otter - known for having a "biscuit like" character. This would give an English Bitter style of beer (if hopped with restraint, say 35 IBU).
For brown sugar flavours, maybe a very small amount of molasses, say 100ml. Or of course you could just use a greater quantity brown sugar, golden syrup, treacle, etc., but this will also increase the alcohol level of the beer significantly. Honey could be added in the last stages of fermentation (or perhaps as priming sugar for bottling), but it does not impart a lot of "honey flavour" when fermented out. I have found that wheat beers made with chamomile tea flowers (specifically dried German Chamomile flower-heads), impart floral, honey*-like* aromas.
Up to 20% Torrified Wheat could be incorporated into the recipe, but I don't think wheat bran would be a good idea since it contains relatively high concentrations of fats and oils which would be detrimental to the beer flavour, and reduce foam stability in the head.
Of course you could go for a "Pastry Stout" style beer, and use actual graham crackers... if you find big sweet stouts delicious.