I'm sure a lot of potential cases would actually be filed in state courts where he would not have much power over, at least directly.

As far as civil vs. criminal, ianal, but

Under traditional English common laws, a doctrine called sovereign immunity prevented citizens from suing the king. Sovereign immunity was incorporated into American law as well, imposing limits on lawsuits against government agencies or employees. source: Forbes.com

So basically, the government has to grant you permission to sue it. If a president decrees that the government is immune in a civil case, there is little legal recourse. (Reminder: ianal, I want everyone to know ianal.)

But the big picture: regardless of whether efforts to interfere could be successful, this announcement will increase police brutality.