Good idea! But I remember I've read somwhere that the blood trait is a recessive one. If so, both parents have to be carriers of the "blood" gene in order for a child to express the blood coloration.
So, if you cross a kumquat with a blood orange, the result will be an orangequat with a very normal flesh coloration (not blood-like at all), let's call this hybrid F1. It's got the blood gene from the blood orange, but it also has a "normal colouration" gene from the kumquat. And the normal gene is always dominating in this case.
So now, you need to cross the F1 hybrid with a blood orange again in order to get a blood orangequat, F2 (2nd generation hybrid). About half of the F2s will have blood colorated fruits, and the rest will have normal fruits. And if you make a cross F1 x F1, there's a 25% chance of getting a bloodquat. It's a long way, but it's certainly worth waiting for getting a real redquat.
The teory seems true, as for example
C-32 and
C-35 citranges are hybrids between 'Ruby' orange and 'Webber-Fawcett' trifoliate and their fruits aren't bloodish at all. Not even light red, or orange, but - greenish. Crosses like this: C32 x 'Ruby' orange / C35 x 'Ruby' should result in getting some blood citranges.
But it doesn't have to be true, and getting a bloodquat might be much easier. And I hope it is! Wish you luck with your hybrids!