I use a water-soluble plumber's paste flux. There will be the original lead based solder under the keypost when it's removed, and unless you remove all that solder, you won't need to add much more. You don't want excess solder squirting out from under the post when you heat it.
I prefer to pre-tin and 'sweat' solder so that no excess solder shows outside. If you try to wick it in from the outside by placing the solder against the joint and heating, there will always be at least a tiny spot of solder left on the outside at that place.
I brush a little of the paste flux on the bottom of the removed post and heat it once with the torch to cause the old solder to smooth out and for the slag to come to the surface. Then clean it thoroughly. The remaining solder should be bright. The same process is repeated for the soldered area on the body tube, taking care not to use too much flux so that the solder doesn't flow out onto the body outside of the original soldered area like others have said. Just heat it enough quickly with the torch so that the solder glosses over smooth. Then clean everything thoroughly. Next, flatten a small piece of new solder - I prefer non-lead silver-tin based solder - between the jaws of a pliers, and snip off a tiny piece. This gets placed between the post and the body when resoldering to make up for any solder lost in the repair process. Lightly brush both surfaces to be soldered with flux, keeping it confined to the solder spot. Use whatever method is most effective to hold the post in position on the body tube. This may be by using the hinge rod (without the keys in place) or it could be a piece of thin bare wire to tie it down. Then heat both the body tube and the post just long enough for the post to settle fully into place and watch for solder oozing out to fill the crevice around the perimeter at the base of the post. If you do this correctly you will see just the smallest line of solder forming a smooth fillet around the base, and it will need no further solder cleanup.
Often though, you may find that the post needs to be reheated to make slight adjustments to the position. Afterwards, clean it thoroughly with warm soapy water to remove all flux residue so that it does not cause corrosion later.
The usual tendency for most people doing solder repairs is to use too much solder, to use insufficient heat applied too slowly, and to do an inadequate job of pre-cleaning and improper flux so that solder blobs up all over.
Do not use rosin flux intended for electronics soldering. It does not work well in this application, and it's difficult to remove.
This is the method, but it takes practice to be able to make perfect invisible solder repairs. You need to be quick and sure with your application of heat too, to avoid causing other soldered parts to come off unintentionally.
