First you will need a FFL. Any FFL will do and a C&R is the cheapest and easiest. This is exactly the same as owning any NFA items: MGs, SBRs, SBSs, or DDs and now "silencers" as they are known to BATFE) that are legal in Missouri.
Next, you will need to determine if your Sheriff or other CLEO will sign off on the forms for you unless you are exempt (Class III, Class VII, SOT etc.)
If he/she will, then it is a "simple" Federal colonoscopy (Form 4), fingerprints, passport photos, pay the taxes and a lot of waiting in anticipation.
If he/she will not, then you have the corporation route. You can establish a corporation to own the silencers/suppressors and not need the photos, fingerprints, and signoffs. You still have to pay the taxes. The corporation would own the silencers so you must get a FFL for the corporation first. You must also keep up the corporation and FFL as long as you wish to possess the NFA items.
A trust will not work in Missouri like it does in some states as a trust cannot have a FFL.
Lastly, you will need another good paying job as NFA is more addictive than crack and a lot more expensive. But think of the money you will save not needing those foam ear plugs anymore.