Hi I'm taking a low dose of estrogen a low dose of a finasteride a blocker, I like the way I feel now and the feel of my skin, I'm not in position in my life where I want boobs to start growing. Does anyone have information about taking estrogen without getting boobs?

Shouldn't you be talking to your therapist and endocrinologist? Or are you self medicating? Which is very foolish

As Cindy has said, self medication is foolish.
Getting boobs are part and parcel of taking estrogen. You take them, you will get boobs.
My two cents worth.

Hugs
Maegan

btw
it will take many months until it will be boobs
and easy way is to bind it while growing - but it can damage them if you want them in future

Emphasising other comments and assuming you are, indeed, taking these legally and sensibly, it boils down to how you are if you think about it.

If you do develop some small bust, you can surely keep it flattened down for a while, at least. Lots of our FtM members do this, very successfully, daily.

What I'm asking you is, what's the worst that can happen?

You like what you have and how you feel. Stay the distance, see what happens.

They shouldn't be growing at a pace thats too uncomfortable or one that isn't easy to hide.  Just double layer, or like they said sports bra

 And mind that, while genetics influence your luck a little, being underweight will slow them down quite a bit. My genetics would have favoured large breasts, but I have to my dismay developed very little... this is partially due to my weight, as I'm 101 at 5'3 - about 20lbs underweight - however, sometimes it's just plain ol' luck. Unless you want to look into it at a very deep level, of course, but it's not easy to see that far...

If you go on hormones, you might develop noticeable breasts, or you might not. It's not something that's simple to be certain about.

It's definitely on of those "your mileage may vary" situations I'm afraid.  They do seem to take a long time to develop, and you can use your female relatives as a rough guide as to final size. 
As Kelly said, weight has a lot to do with it too.  Female runners tend to be thin and flat.

You can send me any you don't want!

Karen.

Huh. I'd like to take testosterone without getting oily skin or a bald spot, but we don't get to pick and choose these things. Maybe male pattern baldness doesn't run in my family, idk. But I try to accept the fate of the cispeople who naturally produce the hormones I'm taking. Everybody's different.

Good luck, but please remember that this is a fuzzy science at best.