Using Solicore flexible batteries as replacement of CR2032
It would take about 100 Solicore batteries to last a year.

The CR2032 is around 240mAh, the Solicore is 10-14mAh. To equal a CR2032 with the high power 14mAh batteries:
$$
\frac{240}{14} = 17.15 
$$
Multiply that by 4 for a year, so 68.6 batteries.  

For the 10mAh ones it's 
$$
\frac{240}{10} \times 4  = 24 \times 4 = 96
$$.  

They may be thin, but are they 100x thinner than a single CR2032?

And that's not even mentioning the minuscule current they can provide...