Flashing the Roof on an Addition

We have a back deck on our home.  Our house has a metal roof and 6″gutters.  We want to screen in our back deck to use it more often (it gets buggy down here in the south) The screen room will have a simple slant roof and we will get the same color metal roofing.  We just had the gutters installed and don't want to take them down.  We want the sun porch roof to be just below our gutters.  The house has vinyl siding. 

The question is…..What needs to be done, if anything, for another type of flashing.  We are concerned with rain hitting the sun porch roof and if it is windy getting  blown upwards to where the two connect. 

The Money Pit Answer

The best way to handle this: Remove the existing gutters, because they'll no longer be needed, and extend the gutter down to the end of new porch roof.  Then flash from the porch deck roof up behind the fascia (trim), and up under the roof shingles above. 
The biggest concern is ice standing, because ice and snow can form over an unheated porch, and snow can then leak down and hit the block of ice.  So you need an ice and water shield to make this connection.  This shield should be extended three feet up into the original roof. 
I realize you're down south, so the chances of excess snow and ice are slim - but I recommend doing this nonetheless.  It's not a solution that's specific to snow-prone areas. Hurricane areas, for example, use ice and water shields beneath asphalt shingles to assure water tightness in the event the roof's shingles blow off.