Does child's income of $640 in BOX 3 of the 1099-misc require a tax return?

[macuser_22]

If that is the only income then no.

2016 Filing requirements for dependents.

Federal Dependent filing requirements: (State requirements may be different)
1) Dependents unearned income was more than $1,050.
2) Dependents earned income was more than $6,300.
3) Dependents gross income was more than the larger of-
a) $1,050, or
b) Dependents earned income (up to $5,950) plus $350.

Or Dependent had net earnings from self-employment of at least $400. 

However, if any tax was withheld, then Dependent might want to file anyway to get a refund of the tax withheld.

Also, a person that CAN be a dependent cannot claim him/her self and must check the box that says that another taxpayer can claim them (whether or not that taxpayer actually claims him/her).

Note: your state filing requirements might be different than the federal.