There will be a wide variety of opinions on this, but I will give you mine, were I the buyer.
First, I would calculate the cash flow as if 3/4 of the new 10% tax came directly out of the salon's profit, and the other 1/4 from the customers. In other words, expect to have to lower your prices by 7.5% to keep the same number of visits. So, whatever the cash flow in the past, subtract 7.5% from gross receipts (that are taxable under the new law).
As for a cash flow multiple, mine would be low, as I do not expect tanning salons to be viable long term. Eventually, the cancer concerns will devalue the business. You could tout the benefits of increased vitamin D production, which is real.
Buying a typical tanning salon is like buying a job, as most have rather low cash flows. Before I could give you my opinion of the multiple, I would need to see the numbers. Let's say the salon had gross receipts of $150,000, $130k of which had the new 10% tax applied. Assume the cash flow to working owner was $60k. I would figure the new cash flow to be $60k - ($130k x .75 x .10) = $50,250. That's close to buying a job, but assuming the equipment is worth $25,000, I would put a value of around $50k on this business, as I don't put much value on buying a job. That's a 1x multiple. If the recalculated cash flow were $200k, I would put a much higher multiple on this. Say, 2x, or $400k. Were it not a tanning salon, I would go even higher, up to 3-4x.
Those are just back-of-a-napkin opinions, without knowing any of the important details. If you post more of the pertinent details, I'd be happy to nail this down further.