This is a question that is best answered on the Jenkins users list, rather than on the developer list. Please ask future questions like this on the user list.
There isn't a series of steps that will prevent those jobs from failing. If the jobs were running on the master previously, then they will likely need to change. Jobs run on a Windows master are frequently invoked with Windows batch commands (Freestyle and Pipeline). Jobs run on a Linux master are most frequently invoked with a Unix shell command. Windows batch is not available on Linux.
If all your jobs use a build tool (maven, gradle, ant, etc.) and that build program is available on the Linux machine like it is on the Windows machine, that increases your chance of success.
Mark Waite