How to find connectors for Densitron TFT displays
I think the connector you need is one like this or similar. They seem to be quite common now, I suspect if you type in "FFC 39" (or "FFC" and then select results with 39 pins) most of the results will be similar. Here are the results I got when doing this on Farnell, I only checked the first two but they both had the same pattern (I selected the second as the first is no longer stocked)

If you check near the bottom of the datasheet, it shows a diagram of a typical FPC pattern which would be used with it. This looks like the diagram in your question, you can check the dimensions to make sure.