My first guess (and it's only a guess) is that the version mismatch is the problem. Tableau has been adding functionality and fixing bugs in Prep at a furious pace, so it would not surprise me if something that works in .3 doesn't work in .1 on Server.
Do you have any idea which specific step is failing?
I downgraded my Tableau Prep Builder 2019.1.3 to Tableau Prep 2019.1.1 and now I don't even see an option to publish to the server. I am getting a little confused about which version of Tableau Prep does what and what is happening with the new naming conventions of the programs.
Tableau did recently release "Tableau Prep Conductor" which is an add-on product to Tableau Server. Not sure if it's the case here but if you're trying to get Tableau Server to run the flow you really need to have the add on for it to be able to run the flow.