How do I watch Kara no Kyoukai?

Since the other answers don't appear to address Mirai Fukuin, I will do that here.

First, you must watch Kara no Kyoukai in release order. That is, 1 through 7 in numerical order, then the epilogue, followed by Mirai Fukuin, and finally Mirai Fukuin: Extra Chorus (a half-hour bonus episode included with the BD/DVD release of Mirai Fukuin). To do otherwise is downright ridiculous - this isn't one of those cases like Haruhi where both release and chronological order have their merits.

Since Mirai Fukuin assumes knowledge of the rest of the series, it obviously doesn't make any sense as a standalone anime. Luckily for you, the sort-of disjointed, vignettish nature of Mirai Fukuin is such that you haven't really had the rest of the series spoiled for you. If you knew what you were looking for, perhaps, but the KnK storyline is sufficiently convoluted that you probably weren't able to pick up on any of the aspects of Mirai Fukuin that spoil the earlier movies. Go ahead and pick up the first movie (Fukan Fuukei / Overlooking View) and start from there.

Later I discovered that [Mirai Fukuin] was a compilation of longer episodes of a series.

This isn't actually the case. Mirai Fukuin is basically an extra, original pair of short stories, not a compilation of the previous movies or anything like that.

Note that there is a compilation movie for KnK, titled "Kara no Kyoukai Remix: Gate of Seventh Heaven", but that's neither here nor there. If, after watching movies 1-6, you find yourself confused about how everything plays out chronologically, watch Remix, which contains short recaps of each episode, in chronological order.

...the story seemed very incomplete.

I should point out that even after watching everything in the right order, Mirai Fukuin will probably still seem incomplete. This is partly because Mirai Fukuin adapts only two out of five short stories in the original Mirai Fukuin novel on which it is based. I haven't read the novel myself, but I hear that the remaining three stories help make everything seem more complete.

There are 7 anime movies of Kara no Kyoukai, in order of release date (which is the same as the order or the Light Novel's chapter/book):
1. Fukan Fuukei - released May 21, 2008
2. Satsujin Kousatsu - released June 25, 2008
3. Tsuukaku Zanryuu - released July 23, 2008
4. Garan no Dou - released December 17, 2008
5. Mujun Rasen - released January 28, 2009
6. Boukyaku Rokuon - released July 29, 2009
7. Satsujin Kousatsu - released December 9, 2009
Source: Wikipedia - Kara no Kyoukai

But if we're to order the movie based on actual timeline of events happening in Kara no Kyoukai's it will be:

Source: Wikipedia - List of kara no Kyoukai Films

I strongly suggest just watch it in order of its release to get the full experience :)

Seems like only the first 4 movies are out of chronological order.

To watch it in chronological order you would have to watch it like this:

• Kara no Kyoukai 2: Satsujin Kousatsu (Part 1) (1995-1996)
• Kara no Kyoukai 4: Garan no Dou (June 1998)
• Kara no Kyoukai 3: Tsuukaku Zanryuu (July 1998)
• Kara no Kyoukai 1: Fukan Fuukei (September 1998)
• Kara no Kyoukai 5: Mujun Rasen (November 1998)
• Kara no Kyoukai 6: Boukyaku Rokuon (January 1999)
• Kara no Kyoukai 7: Satsujin Kousatsu (Part 2)
• Kara no Kyoukai - Epilogue

Al tough personally I enjoyed the story more watching it in release order instead. I don't think watching it in chronological order will fix your experience to much as said on MaL

you won't gain any better understanding by viewing them in the chronological order because each is first and foremost a story closed in itself.