Hi! I have learnt the difference between them. Here i will try to explain to you, although I am not a native Russian speaker:)

Я буду идти на Красную Площадь=I will be going to Red Square.

Here "Я буду идти"-future continuous tense, a long action, process.

Я пойду на Красную Площадь=I will go to Red Square

Here "я пойду"-s<em>imple future tense.</em>

Я позвоню тебе когда я буду идти на Красную площадь.

I will call you when i will be going to Red Square.

(<em>An action happens in the middle of another longer action</em>).

Я позвоню тебе когда я пойду на Красную Площадь.
I will call you when i will go to Red Square.

(An action happens before/after another action).<em>Sequence of tenses.</em>

Hello!

Я пойду - I will go

Я буду идти - I will be going (process)

1. Я отдохну и потом, я буду идти на красную площадь. INCORRECT.

But you may say: Я отдохну и потом буду ходить\гулять ПО красной площади. I will take a rest and than will be going\walking by Red Square.

2. Я отдохну и потом, я пойду на красную площадь. - CORRECT  I will take a rest and than will go to the REd Square

If you will tell somebody: "Я отдохну, и потом, я буду идти на красную площадь", this Russian man will understand you, but it will mistake, it's like: "You to be very beautiful" (Englishman will understand it, but it will be incorrect). So: "Я отдохну, и потом, я пойду на красную площадь" is right form.

Hey Kieran!

I'd support Алексей's and Marina's answers, and to some extent - Kahriman's.
I'll try to resume. Hope it'll help you.

1) It's true that the structure [буду+infinitive] reflects process.
i.e. Сегодня я буду работать до 7 вечера. Today I'll be working until 7 p.m.

2) It's true that you can't say "буду идти в/на...". Not that it's grammatically incorrect, but It sounds very unnatural.
Better use "пойду".
"Идти" (infinitive) - "Я иду"(present) - "Я пойду"(future).

3) Now, for Kahriman's answer. He's brought two examples.

"Я позвоню тебе когда я пойду на Красную Площадь." - is absolutely correct.

"Я позвоню тебе когда я буду идти на Красную площадь." - I'd argue with this one.

As I said, it sounds very unnatural. But, you may say "Я позвоню тебе когда я буду идти по Красной площади.", which means "I'll call you when I'll be walking across/around the Red Square".

I mean, you can't use "буду идти" to say that you're moving to a certain destination. Only when you're moving around some place. It means the same as "гулять по..." in this case. 

Does it make sense?:)

Anyway, I don't think you should bother to memorize how to use this "буду идти", because it's quite uncommon.

Good luck with learning,

Anna

Both are understandable. The second one sounds more natural. I like the Anna's answer but a word of caution for you. Want to be fluent in Russian? Follow very simple rule (actually this rule is applicable to any language out there), big vocabulary and small grammar idea! Focus on learning new words and try to use them rather than memorizing the rules (there are throusands of them) and you don't really need to know them to be understood. In this regard, both sentences seem to me to be fine.

Cheers,

Alex