Looking for a dye...
I don’t think you are going to get a match for 2 reasons. One, they aren’t a dye, they are flames on a weapon. There may not be a true close match since they are handled differently than armor dyes. Two, the flames are 2 toned, orange and yellow and the dyes are one toned.
It also makes a difference what armor type you are as the same dye looks different on each different type. That is, a dye on metal looks different than a dye on cloth or leather.
Your best bet is to look at the color wheel, pick out a likely color, find it on the trading post and preview it on your armor.
http://i.imgur.com/AWPpW.png
I like to use this site to pick out dyes: http://www.dragonsworn.net/dyes/
When you mouseover a color it gives three boxes that show what they look like on different armor classes.
You could try the Fire and Frost dyes though they are getting ever more expensive since there is no longer a source for them. They have gradients when applied to armor, thus getting a multitone effect. There are six of them, with a blue/orange dye icon. “Flame” might work for you. If you search for “dye” on the TP then sort by price, the F&F ones will be in the most expensive end.