Yes, it’s a loanword from German. However, the meaning has changed: usually, the German ‘Reise’ is translated with «подорож» or «поїздка», not with «рейс». The Ukrainian «рейс» is usually translated with German ‘Flug’ or ‘Fahrt’, not with ‘Reise’. At least that’s what my dictionary says.
Рейс usually means one predefined route of a plane or (rarely) a big-disatance bus. I.e. it’s not something you can change, you only choose among available рейси.
I don’t know how well this matches the meaning of the English ‘trip’.
Рейс is a movement over a fixed route of a plane or an intercity bus. It’s a predefined route from one place to another.
Політ is an act of flying. It’s an action/state of moving in the air.
So, you use рейс if you want to speak about getting from place A to place B, and you use політ if you want to speak about being in the air.