Get in form, out of form

Is "out of form" a British phrase in sports?

It is certainly a common phrase in British English. I wasn't aware it was exclusive to or particularly associated with British English, but googling it in combination with NFL or NBA produces few results, mostly from UK sources, so perhaps it is more of a Britishism than I realised after all.

is it different from: I need to get my form right.

Yes. There are (at least) two different meanings of form used in relation to sports and athletic activity.

In the sentence I need to get my form right I would interpret "form" as meaning the form of the body. The closest applicable meaning on a web dictionary would be the shape or appearance of something, although in context it is a little more specific. It would describe the shape your body is in before/during your movements - is your back straight, are your feet close together or spread apart, are your muscles tense or relaxed, and so on. This sense of "form" is commonly used in bodybuilding, but may also crop up in other sports concerned with precise control of the body's posture and alignment, such as weightlifting, gymnastics or diving.

The other sense of form, arguably more common in general sports chat, refers to a competitor or team being in a period where they are (consistently) performing well and achieving good results. For example a football team who have won 4 and drawn one of their last 5 matches is in good form. If they proceed to lose 4 of their next 5 matches, they have hit a patch of bad form.

If I hear

S)He's a bit out of form.

this is the sense I will probably interpret it - (s)he has had a run of poor or mediocre results/performances lately. "In form" or "out of form" typically implies this meaning. If we wish to specify the other meaning (posture/ body shape) we would probably say something like "His/her form isn't quite correct".

You need to get in form. The coach says I need to get in form.

These are fine grammatically, but idiomatically they feel ever so slightly wrong to me. It is very difficult to explain in simple English, but essentially 'form' is an "emergent property". It is a reflection of past events and not something a player or team can 'choose' to be in or out. So it is difficult to imagine a coach telling somebody to get in form, because obviously any sportsman or sportswoman wants to be in form all the time. They don't need telling; it is their aim at all times, by definition. A coach can tell them to get in shape, or practice skills-training routines for longer, or study tactics, or engage a sports psychologist to build confidence - but they can only really hope those multiple factors combine to create the elusive magic we call "form".