Which is the correct tense in the following:

Without more cheap housing, families (will leave/will be leaving) the village and find homes in town.

Hello, Tonyjab!

Both forms are okay.

... families will leave the village and find homes in town.
This communicates a complete prediction. The prediction covers the whole process of relocation as something that will be completely finished.

... families will be leaving the village and finding homes in town.
This communicates a prediction about actions that will be in progress, action in the midst of happening, at some point in the future. The focus is on the time that these changes will occur rather than on the finished or completed actions.

I am very obliged Richard

The thing is that the answer key of the previous question says the simple future form is the only correct answer.

This answer key is wrong, or at least it's incomplete.

I'm interested to know which text the answer key comes from.

Because the verb find in the sentence is not in the progressive, it would be better to use will leave. It would be bad style to put one in the future progressive and the other in the simple future.

I don't see where this was given as an option. There are no examples showing will be leaving together with (will) find in one sentence.

I don't see why this was brought up.

This is a sentence taken from the book Advanced Grammar in Use by Martin Hewings.It has no context.

Yes, thanks Chuncan Feng for noticing the better style for the two verbs: that they be parallel.

I missed that, having focused on only the first verb.

Richard's second sentence had the verbs both in the future progressive, a good style.

The point that the future progressive is possible is correct. But of course, both verbs should be in the same tense.