In the UK, where we use a mixture of metric and imperial units* the full form is more common in speech but some abbreviations are used. This usage definitely lies towards the informal end of the scale and relies on a common understanding.
Both km and kg are abbreviated as kay. This is essentially never ambiguous in context - if I lift "40 kay" it must be kilograms, but if I cycle "40 kay" it must be kilometres. The former is really quite common in some gyms, unheard in others.
Millimetres are often abbreviated to mil. They may be omitted entirely when discussing dimensions in engineering, as they're the standard unit, however imperial units are also often omitted (sheet material may be sold in 8x4 foot pieces). In that case omitting the imperial unit takes precedence, so the laser screen I just designed is cut from "8x4 sheet, 5 mil thick".
Centimetres and grams are essentially never abbreviated (my daughter does read "100 gee" when reading recipes and it sounds odd - but she can get away with it because she's 5). They may be omitted once established ("weigh out 100 grammes of flour and 50 of sugar. Mix together. Then add 50 of melted butter...").
Spelling units out ("kay em") is rare, but perfectly understandable. It's not helpful in formal or careful speech, but isn't an error in casual use.
Summarising/interpreting the discussion in the comments: These shortened forms are handy jargon, but the use varies - so be careful using them. There's never any harm in asking for clarification.
* In theory we're metric except miles (per hour) for road distances/speeds and pints for beer. Certainly our engineering is metric. In practice it's more complicated: a sheet of plywood might have a sticker on it saying 2440x1220mm and be referred to in speech as "8 by 4" (feet).