I know how to get Cloud to go on a date with Barret!
1) Buy the flower from Aeris
2) Talk to Jessie on the train twice and say that you're looking forward to it
3) Give the flower to Marlene
4) Ignore Tifa behind the bar
5) When Tifa asks if you forgot your promise say ...Sorry.
6) When you wake up the next morning talk to Tifa and say that Barret's snoring kept you up
7) Do not get caught on the train
8) When you defeat Airbuster, tell Barret to be strong
9) When you have to save Aeris tell her to wait and push the wrong barrel three times
10) When Aeris asks if Tifa is your girlfriend say "Yeah, that's right"
11) See Aeris home when she follows you to Sector 6
12) You have to get chosen to be the Don's playmate then you have to say "um..." and then "Yes, his name's Barret"
(anybody who makes Cloud almost kiss the Don is wierd)
13) When Marlene inquires about Aeris liking Cloud, say "I don't know"
14) When you rescue Aeris in the shinra building tell Barret to take care of her.
15) After the battle that immediately insues split into a team of Cloud, Red XIII, and Barret
16) Tell Tifa it's kinda hard to get out of the cell
17) Think of Barret first, Red XIII second and Aeris last
18) when you split up at Midgar pick a team of Cloud, Barret, and Red XIII
19) After the flashback at Kalm say "wait a sec" and tell Barret "Beautiful, just Beautiful!"
20) With the party of Red XIII, Barret, and Cloud talk to the girls in the house in Kalm and say to the girl that thinks Mako is convinient that she's full of it and yes that the old life is better to the girl upstairs
21) Make sure you hear the guy at fort condor out willingly and agree to help
22) You can meet Yuffie if you want, but it's better you don't
23) On the ship, tell Aeris I don't know and Tifa I dunno
24) At gold Saucer, take Red XIII with you
26) in the Prison, split into a team of Cloud, Barret and either Red XIII or Cait Sith
27) Take Aeris and Tifa to the Gongaga and ignore them both after seeing Zack's parents
28) If you chose to recruit Yuffie, don't go anywhere near Wutai.
Then proceed with the story as you normally would and when you go to Gold Saucer you'll go on a date with Barret. It kinda starts out a little odd but it's funny toward the end, though when Cloud and Barret are accused of being a couple it'd be better if the programmers made Barret get furious.
Hey, it goes along with the Barret topic! I got all this information via an Affection guide on gamefaq.