As much as you all mock me when I am not around for all of my intarsia love (I know you do, it's okay. I mock you too), I also happen to know that some people wish they knew how to drop the little flower into the back of Kate's Bird in Hand Mittens. I have the emails to prove it. I also got a phone call a few weeks ago from someone in my local yarn store who needed to know how to do it right now! It was a knitting emergency, and I was there in an instant to help.
I've had the question asked enough that I thought it should be answered here (I mean what's a blog for?). Understand, I have no idea if this is the orthodox method. I just figured this out when I wanted a third colour for the mitten's flowers. And you should also know that this is fiddly, and some people would be better off just duplicate stitching the thing, but for knitters like me? Who like fiddly stuff? This is for you.
First, knit the round as usual, and (leaving a tail of about 6-8 inches for tacking down floats later) knit the new colour in the stitches where you want them: in this case, the flower.
Knit to the end of the desired area, and work the background colour for a stitch or two. You need this as an anchor for what you are about to do. Stop.
Turn. Slip those background stitches onto your right needle without knitting them.
Pick up the new colour, and purl back according to the NEXT row of the chart, being careful to slip without working the stitches that are not charted as the new colour. In this case, the center of the flower on the chart is the background colour. Leave them unknit. Just slip them as they are, and let the new colour "carry" across them. Knit the rest of charted stitches that you want in the new colour. Stop.
Turn. Here you see that I stopped, leaving one stitch in the new colour on the right needle before I turned my knitting. That's because in the next row of the flower, that stitch is in the background colour. I'm leaving it there for later.
You have now knit two rows of the flower. Slip all the flower stitches without knitting them onto the right needle, until you find yourself back to where you left the background yarn waiting. Pick the background back up and proceed around the row as usual. In this case, you also have a very long float to pick back up. Don't worry about it because you can tack it down when you weave in ends. Remember that longish tail you started with? That's what it's for.
You have now knit two rows of the flower, but you have knit only one row of the rest of the chart. When you come back around to the flower section (for this row shown, first knit with the background colour that stitch the chart told you to leave be), slip all the stitches you already knit,
and when you get to the flower center where you left stitches waiting for the background colour, knit them with the background colour.
Slip the stitches already knit, knit the stitches you saved, and when you finish the second row of the flower chart, everything lines up nicely.
The trick is to keep track of where you are, the first or second round of this method. I mark stitches off my chart as I knit them so I know if I'm in the first round or second round of the pairing. The Bird In Hands are beautifully suited for this method because you never find your new yarn hanging way out in West Jersey. It's all very civil after all the fiddling.
I hope this gives you ideas. And keeps you from mocking me quite so much.