If I understand the situation correctly...you have a small bead
chain and wish to solder the ends?
Try white out, flood it into the recesses and when dry, scrape it
off where you will solder. In addition to being an antiflux, it
provides a modicum of heat protection. I'd be inclined to pre-solder
the jump ring first. Assemble in a jig of whatever suits, then bring
the heat from the JR toward the chain to join. Cleans up with hot
water or acetone depending on the formulation of the white out.