Well, if you hadn't omitted the definite article, this might be OK - if you were going down to the florist's to collect some you'd pre-ordered, or if you'd just knocked over a vase and strewn flowers all over the floor.
If, on the other hand, you're talking about flowers that are still growing in the soil, then you just pick them. You'd say: "I'm going to pick some flowers."
When I first encountered this mistake from one of my students, I thought it was a natural enough stumble, a one-off error. English phrasal verbs are always a problem for foreign learners (and prepositions - and articles - seem to be especially difficult for Chinese learners). However, I have encountered this particular slip again and again during my teaching here.
And I have found many students who refuse to believe that it is a mistake; some, even, who protest that it must be I who am mistaken. I was reminded of this example the other day because it ties in with the rigid mindset we encounter in fenqing Internet commenters. There is a culture in China of paying extreme respect to teachers - to the extent of regarding them as infallible. This unquestioning and unshakeable trust in the authority of a teacher carries over to textbooks and to the news media. And there's so little exposure to - or even access to - alternative points of view, that mistakes by a teacher or in a textbook (or in Xinhua) are never likely to be exposed.
Somewhere in China there is a middle school textbook that teaches kids to say "I'm picking up flowers". It's a crappy Chinese textbook written by feeble Chinese "academics" who've probably never been out of the country. 20 or 30 years ago, all English textbooks in China were that bad. But things really aren't that much better today. There's still a reluctance to import textbooks from overseas, or to employ native English speakers in the development of domestically published textbooks. The vast majority of English textbooks used in Chinese schools today are deeply, deeply flawed. They teach Chinglish, not English.