I am running a dell 9020 SFF pc tower with and R7 240 video card with display port and dvi outputs.
As far as I am aware, the R7 240 card has DVI-D, which does not support analog RGBHV signal outputs.
You have the SFF version of the card, which unfortunately does not have a VGA video head. HOWEVER, it should have a 12-pin header, near the top of the card, that supports a VGA connector (see pic).
So, one solution might be to find a VGA header with the 12-pin connector and use that. AFAIK the only reason the VGA head is not connected is to save space for the SFF profile. However, I don't know: will it then be available to select in Display Manager / VMMaker?
Another solution might be to use a VGA adapter from the
DP port HDMI port. Someone else might have some adapter recommendations.
These are just suggestions from my armchair, I don't have an R7 240 card.
EDIT: I just noticed that your card doesn't have a DP port as you've claimed above - it is HDMI.