It is permitted to say Brachot while walking but you must be sure to have Kavvana when you say the name of Hashem. There is no Mitzvah to distance yourself for dog feces unless you smell it. If you smell it then you must stop and move away 4 amot from the smell.
Explanation:
The Gemara in Brachot 25a: A person can’t say Kriat Shema in front of human feces nor if front of pig feces, and not next to dog feces when they use them to tan hides.
Rashi explains: It was normal to use dog feces in tanning leather but human feces even without hides are also forbidden since it is not normal to use them for hides.
The Yerushalmi(3:5) say only donkey droppings are problematic forbidden: R Yossi’ ben Chanina you don’t have to distance yourself from animal droppings four amot. R’ Shmuel bar R’ Yitzchak said as long as it is not from a donkey R’ Chiyya bar Abba that is only after it comes from a journey.
The Rosh and the Rabbeinu Yonah both say is forbidden to say Kriat Shema next to donkey droppings not any other droppings. Therefore, unless there are donkeys around, we can assume if you see feces in the streets you don’t have to worry that they are donkey feces. Since they are uncommon.
The Kesef Mishna explains the Rambam that he only forbade saying brachot by animal feces only this which have a bad smell and it depends if people can’t stand the smell.
The Kessef Mishna understood the Rambam that the main issue is the smell of the feces and if it smells then one must walk away four amot and if not then not.
The Shulchan Aruch OH 79:4 writes, “Dog or pig feces if they are tanning hides then you must stand as far way as human feces if not then they have the Halacha of other animal feces who generally don’t ha e a bad smell, but if they do then they have the Din of human feces.”
Usually dog feces don’t have smell when you walk by them in the street, that is why you happened to notice them. If they don’t smell then your brachot are fine.
Whether you should say the brachot while walking is a different issue.
The Gemara in Brachot 51b says: R’ Abahu said (some say it is a Berate) One who eats while waking has to stop and say the bracha standing, if he eats standing, he must make a bracha sitting and if he is reclining and eating, he must sit and eat. The Halacha is that they should all sit and say bracha.
The Gemara is discussing saying Birkat Hamazon which is from the Torah. Even the fourth bracha which was added later we say it sitting down since is part of Brikat Hamazon.
The Rosh adds that one who eats while walking can make a bracha while he is walking since he is concerned about getting to where he is going, he would not make a bracha calmly if he had to stop.
So ruled the Shulchan Aruch in OH 183:11
The Chayye Adom adds that it only if he is eating while waking, if he is siting though he needs to make a bracha sitting.
It seems there is no prohibition to walk while saying brachot and one may say the bracha while walking to he Bet Haknesset, just one needs to focus when he is saying the name of Hashem.
The Shulchan Aruch 191:3 writes that it is forbidden to do work while making a bracha.
The Kaf Hachaim adds that even to eat with table related things rather eh just close his eyes keep his ands still and make a bracha, from a siddur even better.
One is allowed to make brachot walking but a person has to weigh when he will have a clear head when he makes brachot so of course the best idea is to come to shul early to say the brachot properly.
