I've been looking around and I got that the three words can mean "future". Is there a way to differentiate them? Can they be used the same way?
未来 and 将来 are pretty similar to each other. 大辞泉 breaks down the differences under the 用法 section of 「将来」 entry (explanation translated):
将来 and 未来 can both be used in situations where you're talking about the time that will come after the present, e.g. 「将来（未来）への夢」 ("dreams for the future") and 「明るい将来（未来）」 ("a bright future"). 「未来」 cannot be used instead of 「将来」 in an expression like 「私は将来、弁護士になりたい」 ("in the future, I want to be a lawyer"). Also, it's awkward to use 「将来」 in an expression like 「二〇〇年後の未来を空想する」 ("imagine a future 200 years ahead of now"). If it was only 10 years later, 「将来」 would be more common. 「未来」 has a strong sense of a more distinct, intangible future. 「近い将来」 is a common expression, but 「近い未来」 is hardly ever said. The term 「近未来（きんみらい）」 is a recently-coined expression.
To summarize: they're very similar, but when used as an adverb, it's almost invariably 将来, not 未来, and 未来 by default has a farther-off, less tangible connotation.
As for 行く末, it's less common and seems to me to be a more personal sort of future. But I'd stick with 将来 and 未来 for almost all contexts.
I was always taught that
将来【しょうらい】 was a more "tangible" future (like 5 years in the future, 10 years in the future, etc.), whereas
未来【みらい】 was more "intagible", "unknown", and "fantastical" (like "In the future, people will inhabit the moon"; like how people of the 50's thought life in 2000 would be).
I've never heard of
行【ゆ】く末【すえ】 until now, but it seems to correspond to my above definition of
未来【みらい】; more far-off and unknown.
Literally they should roughly mean:
将来 - That which is about to come
未来 - That which has not yet come
This corresponds to the other answers here that indicates that
将来 is a more "tangible" future and
未来 being "intangible". Because for
将来 its path is approaching you. Compare with
未来 which isn't approaching you, in fact its kanji indicates that it will not yet come.