From the documentation of this library:

The library use no interupts of the hardware timers and works with the micros() / millis() function.

This library implements timers in software by polling the micros() and millis() functions. It requires the update() method to be called in loop().

So the start of loop() should be:

void loop()
{
    tickerObject.update();

    if(s == true)

I'm trying to use a Ticker.h to sample an analog input consistently at a frequency of 10khz

It is worth a go but this is a software based solution that is prone to jitter depending on how often the event loop can be called.

use the ticker callback to increment a value. this value can be used as millis() substitute. actually the "millis" is made that way.

write a simple function to give you a delay. this code assumes the callback function is interrupt/event driven like a systick timer in ARMs.

uint32_t ticks;

void callbackFunc()
{
   ticks++;
}

void myDelay(uint32_t del)
{
   uint32_t tempTime = ticks;
   while (ticks < tempTime + del);
}