N.S.
First get her child's book about potties and flushing. One title to check is "Flush!An Ode to Toilets" by Charlie Williams. (Find at amazon.com and is a silly poem about "flushing a toilet").
Or try "It's Potty Time" by Ron Berry (find at most Target Stores) This book literally flushes, and has a giggling childs voice in the background.
Then consider making up a game out of "flushing the potty." Give her a few things that are fun but safe to flush down the potty like cheerios, tissues, etc, but let her do it so she can see for her self she will be safe.
Make a point of telling things go down...they do not come back up. She's probably thinking the spider is still hanging out in the potty, and she might have to see it again. Perhaps if she gets the idea that things that go down, go for good she might not be so afraid.
The only downside of the "flushing" game idea is she might like it so much, she'll want to put everything down the toilet..and you know what that could mean. Use discretion on this of course!