Brass transmits heat much more quickly than lead, so a considerable length or the whole of the piece, e.g., a vase cap needs to be heated to avoid the cap acting as a heat sink and so not allowing even tinning of the object.
When tinning any brass pieces, like a lamp cap, rub it with fine grade steel wool (often labeled 000) until bright, then wash the residue off and dry. Apply flux with a fresh flux brush, and hold the piece with a pair of pliers. Brass transmits heat much faster than lead or solder, so this is a precaution against getting burnt.
At this point you can heat the brass or vase cap with a low heat blow torch to warm the whole piece. When warm, turn off the blow torch and begin applying the solder with the soldering iron. Touch the piece with your hot soldering iron, pause and then start moving the iron slowly and smoothly over where you have applied the flux, applying a little solder all the time.
Alternatively you can work without the blow torch. Apply a bit of solder to the tip of the iron. Touch the piece with your hot soldering iron, let the piece heat up a little, and then start moving the iron slowly and smoothly over where you have applied the flux.
When the whole piece has been covered, wash it, dry, and then inspect for any missed spots or unsightly solder blobs. Apply a little bit more flux and touch with your soldering iron. If you are doing a lot of this kind of work, an 800 degree iron tip will speed up your work.