It is common practice to allow drinking coffee pretty much anywhere. It is also widely accepted to drink unflavored beers. Would that logic allow one to drink beer that is commercially brewed and/or flavored with coffee?
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Second ShimonbM's comment. Practically, as soon as we hear "flavored beer" we get worried what might be in there. Without any further information I wouldn't buy a non-hechshered "coffee-flavored beer" at the store for that reason. However if you're certain the only ingredients are wheat, barley, coffee beans, hops, yeast, and water, and the equipment isn't used for anything else (are you brewing your own?), I can't see the issue.
(With regards to both coffee and beer, the question is raised [Kitzur Shulchan Aruch 38:12] why they're not prohibited under the ban on gourmet-food-cooked-by-non-Jews. The answer given to both is that the main ingredient is water, which doesn't need cooking! I thus can't see how coffee-with-beer would be any different.)
There are very few commercial beers which don't use GMO's (Google GMO beer). There is no way GMO's can be considered Kosher. Mixing coffee and beer should be fine as long as they are Kosher and not drinking until drunken.
http://www.thedailysheeple.com/kosher-certification-program-bans-all-gmo-ingredients_042013 Lev 17:14 "for [it is] the life of all flesh, its blood is for its life; and I say to the sons of Israel, Blood of any flesh ye do not eat, for the life of all flesh is its blood; any one eating it is cut off." Lev 19:19 "'You shall keep My statutes. You shall not let your livestock breed with another kind. You shall not sow your field with mixed seed. Nor shall a garment of mixed linen and wool come upon you."