Clowns and Anemone's have a very specific relationship. Certain clowns generally take to certain anemone's.
Clarkii's generally are compatible with the following:
Sebae anemone
Long Tentacle anemone
Ritteri (Maroon) anemone
Carpet anemone
Saddle anemone
Bubble anemone
That information is from a compatibility chart I looked up. If you have a Sebae anemone, there is a chance it will host eventually. Sometimes it takes a while. Sometimes it doesn't happen at all if the clown is tank raised.
If it is a Haitian anemone, unfortunately they are not typically host anemone's.
Now, on to your questions about why the anemone keeps looking bigger.
It is most likely stretching out trying to get more light. It will give the appearance of growing bigger when in reality it is starving. Your lighting is completely inadequate for anemone's, as has been mentioned. I know...I tried keeping one under 120w of 30w NO tubes. It seemed fine for almost a year when it started getting smaller, and then just started to dissolve. It may take a while, but rest assured it will not survive for any amount of time.