Apple - HDMI VGA projector cannot connect to Macbook Pro
After a few months of experimentation, we found no 3rd party (i.e., non-Apple branded) HDMI <> VGA adaptors which worked well and some which didn't work at all on our Macs. We bit the financial bullet and purchased Apple-branded adaptors and they work perfectly.
We found the same with Thunderbolt & USB <> gig-Ethernet adaptors and Lightning <> HDMI adaptors, too. Remember, you may save $$ purchasing 3rd-party adaptors, but there are tradeoffs in either operation or quality, frequently both.
Most 3rd party adaptors have little or no strain or twist relief in the cable attachment inside the adaptor. We had slews of non-Apple Thunderbolt <> VGA adaptors die after only a week or two of use because the cables literally twisted out of the adaptor body.
Being that VGA is an analog signal, and (Mini) DP / HDMI are both digital signals, an adapter will be required.
Given that you wanted a solution that used HDMI, a powered HDMI port is necessary, which is not be included with the MBP, in addition Apple does not support such a configuration:
Can the HDMI port drive analog displays (VGA displays, for example) using adapters? No. The HDMI port will only drive digital connections (such as DVI) using the adapter that came with the Mac. The HDMI port cannot be used for analog displays such as VGA. You can purchase a Mini DisplayPort to VGA adapter separately to drive analog displays.
I would think you need to do with the Mini DP converter, if VGA output is necessary. Alternatively, it is possible to get a more expensive powered active converter.
On my 2014 MacBook Pro with 2 Thunderbolt ports I found HDMI port to HDMI-VGA adapter did not work, but if I used my Thunderbolt to HDMI adapter then plugged the HDMI to VGA adapter into that, the VGA signal to the external monitor worked fine. Neither adapter are Apple branded, just generic.
I also had to turn off Dynamic Switching of the graphics cards (I use gfxCard Status 2.3) and use Discrete Only to prevent flickering on and off of both monitors. It still happens occasionally, but it's bearable.
EDIT: After a while the Macbook Pro intermittently stopped powering the external display, leading to both displays flickering on and off more often. Maybe I will try an Apple adapter or a different monitor with HDMI input.