Thinking about buying a new bike with a flip flop hub so I can have a good fixed gear on one side and a freewheel on the other.

The problem is, is that the fixed would be about a 18, the freewheel would be the largest I can find, like a 24 if they come in that tooth count. The freewheel would be mostly for hill climbs.

But here's the problem, what about the chain?
Do I have to lengthen the chain to have it over extend to the fixed gear, and then press the tire to the frame to have the higher tooth count?

How does this work?