When referring to a singular drink of Starbucks would it be a 'starbuck' or a 'starbucks'?
Solution 1:
It's "A Starbucks" (or possibly "A Starbuck's"). According to this Wikipedia entry the chain is named after Starbuck, the first mate of Ahab's ship the Pequod in Herbert Melville's Moby Dick. As such the name of the chain is a possessive, not a plural. The same applies to McDonald's where a single Happy meal is referred to as "A McDonalds"
Even if it was a plural it would be the owners who would be plural, not the product. For instance there is a food processing company in the UK called 2 Sisters that owns a pizza chain called Goodfella's. If they had renamed Goodfella's after the holding company when they bought it a single pizza from there would be "A 2 Sisters".
The only case in which you might use the singular is that where the company is named after the product in the plural. If you took one doughnut from a box of Dunkin' Donuts you might call it "A Dunkin' Donut" but one coffee from that chain would be "A Dunkin' Donuts coffee" or, in the short form, "A Dunkin' Donuts" since the coffee is not the product after which the chain is named.