Greenfish Icon Editor Pro has this functionality out of the box. It is a function called "Remove Matte", where you just specify the color component you want to be replaced with transparency. In your case black.
This is the result:
Greenfish Icon Editor Pro is totally free of charge. It is by far the best free icon editor I have ever tried. From the description of the product on the download site:
GFIE Pro is a powerful icon, cursor, animation and icon library editor. Layer support with advanced selection handling makes it a really professional and unique freeware tool for designing small pixelgraphic images. GFIE offers high-quality filters like Bevel, Drop Shadow and Glow; supports editing animated cursors and managing icon libraries. It's lightweight (< 1.8 MB unzipped) and also has a portable version - just unpack it to your USB drive and use it anywhere. A clean, customizable, multilanguage user interface makes it really easy to learn and use.
This will require a little experimentation. As with most things in Photoshop, there are multiple ways to get there.
Eyedropper a solid part of the red cloud to make it the foreground color.
Choose Select > Color Range. Set your Selection Preview to "Grayscale" and the preview thumbnail to "Image" so you can see what you're doing. Uncheck "Localized Color Clusters".
Adjust the "Fuzziness" slider until your grayscale preview matches the image thumbnail. Click OK.
Copy the selection to a new layer using Layer > New Layer via Copy or the keyboard shortcut Ctl/Cmd-J.
Iterate these steps using different fuzziness settings until you have what you want.
Copy your image to a new layer. Optionally, place a layer below with the color you expect you'll be using in any final composite (e.g., a background color or image on a website) so you can see exactly what things will look like.
Double-click the new layer thumbnail to open the Blending Options dialog.
In the "Blend If" section, drag the "This Layer" black slider to the right to remove the completely black background, then hold down Alt (Option on Mac) and drag the right half of that slider further to the right until you see the effect you're looking for:
Select All (Ctl/Cmd-A) and Copy Merged (Ctl/Cmd-Shift-J), then paste wherever you need the new layer with transparent background. (NOTE: If you used the option to place a temporary background below this layer, turn that off before copying so that all you retain the transparency.)
The advantage of this second method is that it is entirely non-destructive, and you can fine tune as much as you like.