How to demonstrate potential for securing external funding in faculty applications?
First, the bad news. The best predictor for the potential for securing funding is a history of having secured funding.

Second, strengthen and tailor your application. If you're a newly-minted PhD, make sure to include grants or awards relevant to your application. For example, you must include the summer research fellowship you won from the university, or the publication award you won from the professional association. Make sure that you provide enough information to assist the assessor. For example, you may wish to explain the point of the fellowship, how much it was worth, and what your outcomes were. I have encountered many examples of resumes of this sort:


Summer 1995 - Summer research fellowship to Jordan


With a little more information, you can make this pop:


Summer 1995 - Summer research fellowship ($15,000). Six-week visit to the field site of Dr James Gilman in Betthorus (Jordan) to assist in excavations and measurements of battlements. Output: one oral presentation and one publication (doi: ...).


The 33 extra words makes a difference, I think. Importantly, to an assessor, it shows that you can turn money into research output.

Third, understand that a demonstration takes many forms. If you've got limited history of grant success (or even if you don't), use this as a chance to show the assessor that you've got a practical plan to attract grant funding. You can lay this out clearly in your research statement. The assessor will be looking for such things as 


a coherent research plan that is related to the research areas of the group (lab, department, etc). You can't demonstrate funding success if you can't articulate a meaningful and important research plan. Plus, no matter how great your plan, if it's outside the scope of the group, then you just look idiotic proposing it because it shows your lack of understanding of the group's goals.
your knowledge of the developments in the field, especially your capacity (or willingness) to collaborate with internal and external partners. Show how your work relates to the work of other members of the group. Show that you have networks outside the group that you might be able to tap.
your understanding of the scope and processes involved in the major granting bodies in your field. You need to give them confidence that you've got a submission plan involving when you intend to develop and submit your applications. Review the application forms and instructions of the major granting bodies. Try to complete them yourself to get the hang of it. If you have access to it, see if you can study the copies of successful grants from your supervisor or other members of the group. Learn how to construct budgets (which is something they barely teach you in a typical PhD).
your resilience in the face of knock-backs. Grant submission is better seen as a cycle, not a path. The latter has an end, implying that if you don't get the grant, you drop the idea and move on. It's more realistic to consider grant submission as a means of refining a research idea and that rejections come with valuable comments that allow you to improve for the next round.


Fourth, be aware of the start-up costs that you will need to fund your work. Unless you come with your own funding already secured (in which case this post is really irrelevant to you), you will need to do some work on your own while you submit applications. Many groups provide start-up funding, but this is capped and you need understand how this works.

Fifth, be careful of (over)confidence. Receiving external funding is hard. Don't give assessors the impression that your work is so obviously the next big thing that hiring you will result in money falling out of the sky. That might be the case, but more likely than not, you'll simply come off like an airhead.

I'm sure there are many other points, but these are the ones I can list before I head to an appointment with a dentist.

Good luck to you (and to me)!