HTTP Strict Transport Security (HSTS) doesn't prevent you from changing your DNS records to point to a different IP address, it just prevents HSTS enabled browsers (that have seen the HSTS header or have been preloaded, i.e. Chrome) from attempting to connect via HTTP (vs. HTTPS).
All it does is cause the HSTS capable browser to change a request for http://example.com
to https://example.com
before sending the request, thereby ensuring that no information is ever sent in the clear.
The Cloudfare warning just tells you that when you change hosting companies, you need to make sure that you also have a valid SSL installed at the new site.
Because you have the valid SSL certificate at the new hosting location, you are good to go. Just update your DNS and carry on!
If you are keeping SSL, there is no reason to disable HSTS. On the other hand, not having HSTS on an SSL capable site makes that site less secure because traffic that would have been prevented by HSTS from flowing via HTTP is able to traverse the Internet in the clear.
As far a HSTS "preloading," this is the process of companies like Google preloading the HSTS header in the Chrome browser (as opposed to the browser having to have visited the site once before it stores the header). Like all HSTS header information, preloaded HSTS information is stored by hostname, not IP address. You are always free to change the IP address at which the site is hosted. On the other hand, dropping SSL after you have enabled HSTS is what will make it hard (if not impossible) for some users to visit your site.