How to modify a quick bread recipe to add spice / tea flavors?
I just noticed that your recipe uses water. That's an ideal way to get tea flavor into things - you can replace it with concentrated tea. Assuming you use teabags, you should be able to steep two in that 2/3 cup of water. Tea is a fairly subtle flavor, so you may not taste it too much in the bread, but this is easy and doable with what you have! There's also instant tea, if you want to try to boost it - but it of course won't be as good as real, fresh tea. (You could buy chai concentrate, but I think it's usually about double strength, so not really better than you'll do on your own.)

I'd then replace the spices normally in your recipe with chai spices. If you've ever made chai from scratch, you could use that recipe as a guide, but it sounds like you might not have. There's an awful lot of variety here, from region to region, and in Western variations; you could search around online for chai recipes that appeal to you. I'm not an expert (I'm from Texas!) but from what I know, here are some common spices, with the most standard ones toward the top:


cardamom
cinnamon
fresh ginger
black pepper
fennel
cloves


Cardamom is pretty much required, and that'll help give you a flavor very different from your usual spice blend. I'd mix/grind up the spices separately from the rest, smell them to see if they're what you're looking for, and adjust as needed before mixing into the rest. Aiming for a similar total volume of spices to that of the original recipe should work fairly well. It might be a bit spicier, since you'll also have the tea, but that's probably fine. (Fresh ginger obviously won't go with the dry spices, if you use it - maybe a teaspoon or two minced?)