Valid reports slow down your honor growth drastically. So, to gain honor requires not being validly reported.
Reports seem to be considered valid if there is ANY negativity in the chat log. That means that there are some common behaviors that on their own is not enough to earn a penalty, but is enough to remove your honor.
Therefore completely avoid:
Saying that you're reporting someone.
Asking for other people to report someone.
Accusing anyone of afk/trolling/feeding/flaming/ect.
Threatening to afk/troll/feed/ect.
Saying that you're muting someone.
Linking anyone's KDA to highlight their deaths.
Using EZ or any of it's offshoots at any point in the game.
Insulting anyone. That includes "Just saying" or "It's the truth, not an insult"
/Edit 1
From careful consideration of Red posts and all the honor milestone posts (when honor was new and people talked about the specifics of when they hit 3/4/5) it seems very likely that being honored counts very little toward honor growth, and the biggest honor gains are from playing a game and the "everyone on the team honored someone" bonus. So don't worry about farming upvotes in your matches.
/Edit 2
If you want to criticize a bad play, that can also be considered negative, but if you word it as, "Next time do XXXXX" or "Next time wait for my ult to be up" ect. Communicating a plan that will help you win/do better is what chat was made for, so using it that way is always ok.
Saying, "You should have.....(waited for ult) (warded first)(smited better)" can be flagged as negative by the IFS, because the past can't be changed. Remember to focus your comments on the future, not the past.
