I need ideas for a fast growing, trellis climbing, flowering plant...

[barnyard pimp]

Yes, it can get out of hand if it is not maintained. The trumpet honeysuckle is also good. I think the japanese type is the least expensive option. I have worked with both. I built a huge pergola about 10 yrs. ago. The lady wanted it to be completely covered. She used the trumpet type. I boils down to what you like. I think either of them will in the end take over the fence and give you plenty of privacy. It has an awesome smell too!

 

[Happy Chooks]

How about Star Jasmine? It's really fragrant though, so you have to love smelly flowers.

 

[TheSitcomGirls]

I would stay away from the Wisteria. It produces pods which are poisonous to dogs and horses. I'm not sure about chickens.

Did anyone mention roses? I have a climbing red blaze variety that I planted two weeks ago and it has grown a couple of feet already. I also have a yellow climber that I paid $5 for through the mail. It was a stick when I got it.

Now in year two it is already this big: (With very little care other than some copper fungicide dust in the spring if we get a lot of rain.