(continued ...) For tubes, use a cylindrical plastic bristle brush on a long flexible twisted metal wire. You can find these at home brewer outlets. They are used them to clean carboys (5 gallon glass brewing vessels with a small opening for a cork). Whatever shape and configuration use plastic bristle brushes. Be sure to leave no plastic bristles behind. Do not use steel or brass brushes. Brush and vacuum as you go. If possible, vacuum from the bottom and brush from the top. Do not use any cleaning solutions or liquid of any kind on the combustion side of the heat exchanger.
Now examine what you vacuumed up. If you find any rust particles (reddish to dark brown), even if the heat exchanger is stainless steel, there may be a hole in it. If this is a boiler, re-assemble as required. On the water makeup line, add a water meter. Run the boiler as you normally would and check the water meter daily for a week and then each weekend. If you see water being added and find no leaks, then the heat exchanger has a hole in it. The water is leaking through the hole and going up the flue. This will only get worse but you may have some time to plan. Think about moving yourself into the third group and plan a complete boiler replacement.
If this is a furnace, re-assemble as required. Purchase a carbon monoxide (CO) sensor and mount it near to or above a heat register outlet, closest to the furnace. You should already have a CO sensor but if you don't this is the time to get one. And you with the boiler, you should have a CO sensor too! Run the furnace as you normally would. If the CO sensor registers anything other than zero, you are in crisis mode; sorry. Turn off the furnace and do not run it again. Replace the furnace today or as soon as possible *1 *6. ...