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Many Flag and Pennant users recommending a very straightforward design - Amidon BN73-202 binocular core with 3 turns for a primary and 12 turns for a secondary winding.

Wind the transformer with the low impedance winding first, and put the high impedance over it. For the primary, a plastic coated wire can be used, the enameled wire used for the secondary does not need to be wound directly over the ferrite. This will allow you to wind an extra turn or so, and using an impedance bridge, pull off turns until you get the exact impedance ratio you need.

A single turn through the core
A single turn through the core

The primary winding
The primary winding

The complete transformer
The complete transformer

Be careful when winding so as not to damage the enamel insulation. The transformer is probably the most critical component in the Flag or Pennant RX antenna. If you have a problem with a Flag or Pennant, look to the transformer!