There's a few issues with the usage. You've spaces between the operator and the values, there should be no spaces except for the include operators. There are no quotes around your value, there should be. Also no you don't place brackets around them. It's also best to use "and" or "or" instead of the shortcut "&&" and "||". Your substitution should be as follows.
[cb:if cb_2014llf>="250" and cb_2014vopac<="750"]
<img src="images/icons/medal_plat.png" title="Platinum Status" height="14px" width="14px">
[/cb:if]
Please note single quote is not valid in an html element. It should always be " and not '. I've also corrected this in the above example. I also assume you meant you want the value within 250-750, but you were checking that it was >= both 750 and 250. It now checks that it's >= 250, but <= 750.
Please see the below tutorial for further substitution usage information.
www.joomlapolis.com/support/tutorials/107-use-cases/18353-using-substitutions-throughout-cb