Can you do a DCF for a company with negative free cash flow?

Yes. A DCF values the cash flows a business will generate over its life, so negative cash flow today is not a problem as long as there is a credible path to positive cash flow. The negative years simply reduce value.

The main change is the projection period. For a high-growth company burning cash, a five-year forecast might end while it is still losing money, and a terminal value based on that year would be meaningless. So I extend the forecast, often to ten years or more, until margins and growth reach something like a mature steady state, and only then calculate terminal value. I build the forecast from drivers: customer or revenue growth, gross margin, how operating expenses scale, and capex and working capital needs.

The result is very sensitive, with most of the value in terminal value, so I would show scenarios, such as base, upside and downside, plus sensitivity tables on growth, margins and discount rate. I would also check whether the company has enough funding to reach profitability, since future dilution matters to equity value, and cross-check against EV/revenue or EV/gross profit multiples for similar companies.