"should be coming from" is correct and usable in written English.
You can use it when expressing what you think the source of something should be. For example, "This help should be coming from the government, not private organizations."
Another round of ads should be coming from her company shortly.
In fact, the more skilled your people are, the more ideas and strategies should be coming from them.
The Lib Dems passed a motion saying that 10% of the government's revenue should be coming from green taxes by 2015.
Some observers have pointed out that daily briefings on preparations for Gustav, which should be coming from the Federal Emergency Management Agency — which is, you know, supposed to manage emergencies — have been coming, instead, from the U.S. military's Northern Command.
If there's a particular surprise here, it's that this Anglophilia should be coming from New Jersey, a place that – if we are to believe what we see on television – is populated chiefly by neurotic mobsters and sexually rapacious young people with waxed eyebrows.
More news should be coming from the company shortly.
It may be that packing is particularly difficult for me because my earliest ideas of what packing should be came from the films of the 40's where stars like Anne Baxter or Loretta Young made it look too easy.
Fresh air should be coming in from the front and top, and get exhausted out the back of the computer.
Also, a multiplexer for each line should be coming in from all the sites, and a shift so that the sites don't override.
If it is sitting correctly, most of the time there will be a thin strip on the saddle pad that the saddle sits straight above, and should be coming out from directly underneath the pommel.
The wind should be coming toward you, not from behind.
