This image looks like the manufacture was trying to give you 4 stamps in one.
One thing I might would do (if you can---- if it's unmounted or a clear stamp) is cut the flowers apart from the leaves--thus you'd have 4 stamps after separating them---that way you can stamp the leaves and then stamp all tulips or all daffodils etc (or mix them as well, as it is currently). If you cannot cut the stamp (or do not want to go through the trouble), I would only ink parts of the flower image----the flower heads are floating above the stems so you do not have to worry about getting the flower attached to the leaves perfectly.
I can see what Heidi means that it looks like a stencil....that could give you ideas to google and look on Pintrest for how flower stencils are being used and then use similarly.
To me it reminds me of silhouette stamps....and for those types of stamps, I usually do one of the following:
1. heat emboss the silhouette stamp and then color over the embossed image with distress inks or watercolor---to me, the emphasis here is not really coloring the flowers but rather coloring the BG and the flowers are showcased in front of that BG.
2. make a BG of any technique (you could use the bargello, for example) and set aside. Stamp your flower stamp onto a separate CS of any solid color (and with any ink color or type) and then either fussy cut or die cut the flower image out of the CS. Place the prepared flower imaged onto the BG.
3. if you have stamp markers----color the stamp itself with the stamp markers before stamping (remember to breath on the stamp first before stamping)---and in this case, the use of the stamp markers is to color the flower image itself, so I'd then use a neutral BG as the base to stamp the flower onto.
4. if you have watercolor pencils or watercolor paints, you could color around the embossed image and then apply water---similarly to what you were doing with the colored pencils. I was thinking with this idea, that maybe using a different media combined with your original idea of coloring around the flower might achieve something you like more (at least sometimes it does for me). Also, I would stamp the flower again as you did and instead color the "sky" or BG and see if you like the results more.
As with my suggestion of googling stencils, here is a google search for "silhouette stamps cards"
HERE, but click on IMAGES as the top and scroll through the images and notice how they are used.
And my one last idea, is to search online for that stamp itself--if you know the name or maker--and see what others have done with it--that is if anyone has posted anything.
HTH!
