Hi BMS
.
I think I have what you want to do as either a dipole mounted inside a flag pole ( I am assuming it is non-metallic) or to use the (non-metallic) pole to hold a vertical wire.
I am not familiar with the flag pole, but if it is metallic- forget both options.
.
However, that said, you can mount a dipole inside a vertical non-metallic pole, but you will have to run its feedline-- coax or what ever, off the center at a 90 degree angle, and run it for a considerable distance. It will not work other wise. If it’s a covert/hidden antenna you are trying to achieve, this will probably defeat it.
If you are versed in antenna designs you can construct a coaxial fed vertical by folding back the coax over the feedline, and placing it all within the vertical section of the mast-- but that topic is far beyond the discussion here.
.
Better still, is to run a heavy gauged wire up the inside of the mast, and use a tuner a the base. By using, as you mention'd, ground level radials, this 20 foot section can be resonated over a wide band of frequencies, at least 3.5, maybe 1.8, upwards to 30Mhz’s. Such a tuner can be manual, but a logistics pain- each time frequencies are change. Better, is an auto tuner, similar to those used in the maritime service…. Look at what Icom makes-- I use these for this very purpose- matching random vertical antennas....
But, and this is very important-- if you go this route-- mount the tuner **At the Base of the Vertical !**- tie it directly to your vertical radiator and the ground radials-- no coax etc., between it and the radiator !
.
.
Here is a simple formulae for calculating antenna lengths- let’s say- in your case: a 20 foot mast is approximately 6 metre’s. If you wanted a quarter wave vertical, this is ¼ of the desired wave length at ~24 metre’s -- and close to the 20 metre band.-- it could become a 20 metre band antenna. You will need to use more exacting calculations, however--
.
…ie: for a half wave dipole---
.
Length in feet = 491.8 x K/ freq Mhz.
.
………..K is determined by wavelength divide by radiator diameter… (in most cases 0.96 will do for HF dipoles)
.
.
I hope this points you in the right direction, BMS..
.
Good luck… further questions?.. Please ask away….

.
.
…………………..CF