Is dual residency visa allowed in Oman and UAE?

I can't speak to Oman labor laws but generally most GCC countries frown on dual residencies.  To be clear, they frown on dual "WORK" related residencies.  However, quite a few people have those.

The only problems I have seen is with UAE and Saudi.   Sometimes they ask you to cancel the other residency before you can apply for a work visa with them but not always.

However, you mentioned that you will start a company in the UAE. This means that you will get an "Investor" or "Businessman" visa.  These are not counted as work visa i.e. employment.   So it is perfectly ok to have two.  Even I have this situation i.e. investor visa in Bahrain and work visa in Saudi.  And have had UAE and Bahrain in the past.  My mother had both as well.

Also, if you are not living in a GCC country but visiting it to do activities like business meetings or consultancy through contracts with local companies; you don't need to have a residency there to do that.  It is only needed if you either live there OR are employed with a company there.