flail (v): 1.1 Flounder; struggle uselessly.
Your boss initially used "flail" to tell you that, if you have no idea how to do something, you should hand it off to someone else. Otherwise you're just wasting time. It's not a good idea to use "flail" to describe your own efforts, as it suggests you will simply struggle and achieve no useful result.
Instead, use a more positive term that implies that, even if you do not make progress, you still are putting in a meaningful effort.
Let me work on the problem for a bit (before I ask someone else for help.)
Let me wrestle with the problem for a bit.
Let me plug away on the problem for a bit.
Let me sweat over the problem for a bit.
along with various others. These all imply you are making good use of the time, even if you may eventually fail to achieve the desired result.
As I mentioned you can use "flail", if you are speaking with a kind of ironic "false modesty", knowing that your effort will succeed, but wanting to sound humble.
For example, suppose I am an excellent artist. A friend asks me to paint a portrait of her relative. I know I will do a good job, but in order not to sound boastful, I might say:
Well, I suppose I can flail about with my paints and brushes, and hopefully the picture won't be complete rubbish.