VGA Output for 640 x 360 (16:9) Display for LCD monitor
It depends on the sink (monitor) but most computer displays and display controllers accept VESA standard timings, either from the VESA Display Monitor Timing (DMT) or VESA Generalized Timing Formula (GTF). VESA is the Video Electronics Standards Association, a standards body for computer display standards. In contrast, most displays for televisions/broadcast/movies accept CEA timings, specified in EIA-CEA-861. The relevant VESA documents were open to the public until recently and are still readily available; CEA-861 is available for a fee but there are older revisions somewhere out on the interwebs.

VESA DMT and CEA-861 are both tables of resolutions, giving the standard timing for common resolutions. However, IIRC, 640x360 is not in either, and therefore VESA GTF is your best bet (unless your sink has an EDID that tells you otherwise). My copy of the VESA GTF (it's just a spreadsheet, easily found with Google) tells me 640x360@60 corresponds to an Hblank of 7.447 us and Vblank of 0.581 ms, among other things. I would highly recommend glancing over the VESA DMT and playing around with the VESA GTF spreadsheet, it's quite educational.

Note: the VESA free standards used to be open to the public. Sadly, it seems that is not the case any longer and you now have to be a VESA member. Also, there is a Linux utility aptly named gtf which will happily calculate GTF timings for you.