If it wuz me, I would tint a high hiding primer or white tint base paint your burnt orange colour rather than have it tinted gray.
Now, you don't need to know the rest, but it explains why people recommend painting with a tinted primer first, why TiO2 hides well and why you can improve the hide of a primer or paint by "toning" it a darker colour:
(I wrote and rearranged this post several times, so if it's a bit disjointed or I repeat myself, that's why. Also, before anyone barks at me, I'm fully aware that other factors besides the amount of TiO2 affect the hide in a paint, but I'm just wanting to explain why people use tinted primers as their first coat when changing colours.)
When you don't get complete hide after painting over a substrate of a different colour, what's actually happening is that incident light is travelling through the paint film, reflecting off the substrate, and coming out of the paint film to hit your eye. Some pigments in paint help prevent that by either: a) bending the incident light so that it travels a longer path through the paint film, or b) absorbing light so that there's less light hitting the substrate and reflecting off, and less making it out of the paint film as well.
Unless you know of a high hiding primer with lots of TiO2 in it, it may be safer to spend a little more and buy a top quality flat PAINT and have it tinted in the burnt orange direction. The reason why is that primers don't always have enough of the white pigment "Titanium Dioxide" TiO2, in them to provide good hide. It's the titanium dioxide that promotes good hide in primers and paints, and all things being equal, the more TiO2 in the can, the better the hide. But TiO2 is a relatively expensive pigment, so the more there is in a can, the more that can is gonna cost. If you can find a high hiding primer, then by all means, have it tinted your burnt orange colour. But, if you don't know if a primer hides well, play it safe and spend a little extra and have a can of a top quality high hiding flat white tint base (paint) tinted your burnt orange. The high hiding white tint bases (which are paints before tinting) from good names like Benjamin Moore, Pratt & Lambert and Sherwin Williams will always have lots of TiO2 in them for good hide.
Titanium dioxide is the second highest hiding pigment used in architectural paints, second only to black.
People erroneously presume that primers all have enough TiO2 in them to hide well, so they think they can hide the underlying colour with a coat of primer than a coat of paint, but that's simply not true. idea of priming first is that one coat of primer will hide better than one coat of paint, but that's not always true.ide well, so the reason why people suggest painting over a colour with a tinted primer is because they think the primers will have the white pigment titanium dioxide (TiO2) in them. TiO2 is the second highest hiding pigment used in architectural paints, second only to black. So, the idea is that by painting over a coloured substrate with a primer, the TiO2 in the primer will hide better than a coat of paint. Truth is, lots of primers don't have enough TiO2 in them to hide well. Zinsser's Bullseye 123, for example, has LOUSY hide, so tinting it a yellow or red colour is a waste of money, labor and time because it won't hide an underlying colour well to begin with.
So, if you are going to prime with a tinted primer, make sure your primer has lots of the white pigment TiO2 in it so that it will hide well.
If you don't know how well a primer hides, what you may want to do is paint over your dark colour with a coat of a top quality flat white tint base PAINT (tinted or not). If you get a quart or gallon of the highest hiding flat white tint base from Pratt & Lambert, Benjamin Moore or Sherwin Williams, you're going to pay more than you will for a primer, but part of the extra cost will be due to the much higher amount of TiO2 in the can. TiO2 is a relatively expensive pigment, so no one's going to give it away free. Higher priced lines of paint will have better binders that dry to a harder film, harder extender pigments that stand up to scrubbing better, more TiO2 for better hide, and better additives in them for less spattering, better wetting of the surface, better self levelling, more effective biocides, etc.
The only problem with "priming" with a high quality flat paint is that you don't benefit at all from the better binder and better everything else in the can because you'll be painting over that high quality paint with another paint. So, if you can find a high hiding white primer with a lot of TiO2 in it, use that instead because then you're ONLY paying more for the extra hide, and not for everything else being better too.
Now, titanium dioxide has very good hide because it has a high refractive index, meaning that it bends light MORE than other white pigments do. As a result, incident light traveling through a paint film that's only .006 inches thick gets bent at a larger angle so that it travels further LATERALLY along the plane of the paint film, with the result that more of it is absorbed by the paint film and less of it hits the substrate and reflects back to your eye. Also, because TiO2 bends light though a greater angle, it takes statistically fewer refractions to bend incident light through a 180 degree angle and send it back from where it came (out of the paint film). Thus, again, less of the light you see is reflected off the substrate, and that means you see less of the colour of that substrate, which means better hide. If the refractive index were lower, incident light would take a straighter path through the paint film, so it wouldn't travel as far in the paint, so less of it would be absorbed because of the shorter path and more of it would hit the substrate and reflect back out again. That would result in you seeing more light reflected off the substrate, which would mean the paint film doesn't hide the colour of the substrate as well.
But, because titanium dioxide only reflects and refracts light, and isn't very good at absorbing light, you can greatly increase the hiding power of a paint by "toning", and that is to add dark pigments that are great at absorbing light, like the black and raw umber pigments. A "high hiding" primer or white tint base paint will have both lots of TiO2 in it and some dark pigments in it to absorb light. So, the TiO2 bends the light so that it travels further through the paint film, and the dark pigments in that film absorb that light, so even less incident light is likely to reflect off the substrate and make it out of the paint film alive. You don't need to add much dark pigment to get a large increase in hide, but you do get more hide the more black you add because it does hide better than TiO2.
So, hiding is a property of the paint you're applying over a substrate, not a property of the colour of the substrate. That is, it'll take as many coats of your burnt orange paint to hide a cream colour as it will to hide a green or blue or grey substrate. But, because that cream colour is mostly a white colour, the light that does reflect off the substrate will be mostly white and will result in your seeing a slightly lighter version of your burnt orange colour. And, people find this more acceptable than a greenish or blueish or greyish version of the colour they're shooting for. So, a grey first coat will hide the colour of the substrate better than an untinted first coat, but it takes just as many additional coats of any paint to hide the substrate colour, regardless of what it is. Tinting your first coat with the top coat colour helps by putting more of the colour pigment you want between your eye and the substrate, so that tinted primer ALSO acts like another half coat of paint.