I'm trying to transmit this message, but I'm not sure what is the correct way to do so. In short words I'm trying to give an order.
"Keep away from your phone" is grammatical, but not very natural. A better way to say this would be "Stay away from your phone" -- meaning "keep a large physical distance between you and your phone". This is a strange thing to ask someone to do, though (unless you think the phone will explode).
"Keep away your phone" is not grammatical. To keep something away means that it is trying to approach you but you prevent it from approaching you. "Making loud noises will keep bears away." "An apple a day keeps the doctor away." But a phone is not alive or animate, so it cannot try to approach you.
To convey the meaning you want, I would say "Keep your phones put away". This means "it is OK to have your phone near you, but it must stay in your pocket or handbag or desk". (I suppose you could say "keep your phone away", but it is less natural.) You could also say "Keep off your phones". This would suggest that it might be OK to take your phone out, but you should not actually use it.
Keep (or stay) away from your phone would be the proper way to order someone. Both sentences have an implied you in front of them. You keep away from your phone and You keep away your phone. But in the second sentence you are implying that the person should keep their phone away, rather than saying they should keep away from their phone. Usually you aren't ordering someone to keep their phone away from them, but rather are ordering them to keep away from their phone.