When you mix the streams, do you expect to have any condensation from either stream due to differences in pressure or temperature?

What is the heating value of the streams and do you need to add supplemental fuel?  Burning them in a single burner should be feasible, as long as the burner design can accomodate the expected range of operating compositions and heating valves, this could be as extreme as 100% vacuum off-gas to 100% acid gas from the SWS.

We have an VDU off gas burning in one of our units. The problem is it has a very low pressure & LHV, The gas cant be sent to the flare so we burn it in the heater. The Heater does not depend on the off gas as a primery fuel. Natural gas is used as a primery fuel. All burners burn the two gasses but they dont mix inside the burner. The draft created in the heater is required to suck the off gas and burn it. The burners have separte holes for each gas.

Flame arrestors are used also for the off gas.

When burning off gas from a SWS unit, ther may be times when the tower gets upset from varois factors, is there a potential for hydrocarbon to get into the stream? If so then you will need to be prepaired for it to be in the overhead off the SWS Unit. Is the heater you are burning the off gas in permitted for this?

The biggest worry I'd have is a large volume of hydrocarbon vapor reaching your furnace. At a minimum it will upset your oxygen balance.

What u r looking for should be absolutely possible if the piping  and furnace material+hydraulic design permits it.
U need to analyes the problems for this.