Machform has some ability to backup and restore data - but I forget if that includes the forms / or associated submissions data.
I would see the simplest method being to copy (that is, download from old site, then upload to new site) the Machform files from your current site, to the new site. Then export the database from old site, import to new site. (such as using phpMyAdmin).
Remember to change the configuration file detail on the new site, to the new database details.
That should be all you need to do but if unsure about any of this perhaps Appnitro could also assist you doing the transfer, suggest putting in a support ticket to them.