How can I best estimate a company's contribution to GDP? Would revenues be a good proxy variable? If not, what are the other proxy variables that I can use?
As a comment noted, value-added is the way to go. And how do we measure value added at the level of an individual firm? 

It is 

$$\text{Value-added} = \text{Wages and Salaries incl. Insurance}+\text{Depreciation}+\text{Profits before Taxes}$$

"Wages and Salaries including social security fees" is the reward of Labor, while "Depreciation plus Profits before Taxes" is the (gross) reward of Capital.  

This makes sense because if one views GDP from the "income" angle, it goes to these two aggregates of productive inputs, "Labor" and "Capital". 

All other expenses that appear in a company's Profit &amp; Loss Statement are "third-party costs", or value that other productive entities create.

Depending also on the jurisidiction, in most cases Labor costs, Depreciation and Profits before Taxes can be found as separate items in the financial statements of a company.