I have a problem with water from flats upstairs entering my kitchen through the pipes, according to their landlord there is no blockage in the drain, it only seems to happen when they use their washing machines. Water drains from my kitchen fine, any ideas to the problem?

There is a partial blockage in the drain below your kitchen sink. Apparently the blockage is enough to cause a problem when the upstairs residents use the washer but not during other uses. A clothes washer pumps out water at considerable speed and force.
Snake your drain.
I believe you use the term rod for clearing a drain. We say snake.

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according to their landlord there is no blockage in the drain

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And he knows thus because? Harold's bang on! The blockage isn't large enough to block regular kitchen drainage but a washer pumps high volacity discharge the pipe is overwhelmed. His solution is the only one. Have the drain snaked. Good luck, Tom

My guess is that the landlord snaked the drain and came up with nothing. If that is the case, tell the landlord that he did not go far enough or did not work the snake long enough to clear the partial blockage... ;)

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according to their landlord

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Suspect that units have different owners.

I definitely meant the landlord from the unit upstairs.. always good to clarify anything questionable, Harold! Thanks