"We live in a world of cowards. We live in a world full of small minds who are afraid. We are ruled by those who refuse to risk anything of their own. Who guard their over bloated paucities of power with money. With false reasoning. With measured hesitance. With prideful, recalcitrant inaction. With hateful invective. With weapons. F@#K these selfish fools and their prevailing world order." Tony Stark
While I am more of an Eddie Brock fan, I will not be caught dead badmouthing Flash's tenure as Agent Venom. His original run by Remender is probably fighting toe-to-toe with Cates' current run to see which one is the best Venom story ever (and for some, there is nothing Cates could ever do to top Remender) and I agree with why it is so good. He reinvented the character and identity of Venom entirely, had great stories, was an amazing character. It was great, really.
As for him being pushed too hard? Eh, he was Venom. Real talk: Venom has always been pushed too hard. No matter if the host was Eddie, Flash or even bloody Mac Gargan. Venom has always been up there because he is a surprisingly recognizable face, and I don't think he was as bad as 90s era Eddie Brock, for example. Sure, he was in a good deal of books, but it never bothered me. He always felt natural -- Except in Guardians of the Galaxy, that is.
So overall. I don't think there was anything particularly bad about Flash and his push. He rapidly became a beloved character, and I think most of the fanbase was happy to see him around in other books, since he rarely stole spotlight.