There is nothing wrong with laying on your tummy whilst pregnant if you are comfortable to do so. I was able to lie on mine until 33 weeks. I was also massaged in this position at 28 weeks.

You need to tell any massage therapist that you are pregnant and how far along you are, but there is little to no risk if you are out of the first trimester. Many will not massage first tri women, but this is a cover their arse kind of thing. Any decent and properly trained therapist knows exactly where to and where not to touch a pregnant woman.

Your concern should be the oils they will use. Again, telling them you are pregnant will ensure they use neutral and safe oils on you.