So we have a website, where in PHP script that send, via apache mail server, around 1k emails a day, once in a while our IP get flag as spammers.
I am looking in a way 3rd party host to be our mail server in order to avoid getting our IP flag as spam.
Any suggestions
There are a lot of providers that supply email sending service. I work for Mailjet but you could also try Sendgrid or Mailgun and see which one works better for you.
Most of them have a free tier that will let you test the service, and they all work pretty hard (I know we do anyway) to ensure the best possible deliverability for your messages.
You might want to check out this comparison of email-as-a-service providers as a first approach
What you're looking for is email service provider, try them:
Your ISP may already provide you with access to its SMTP service. Spamblockers that analyze the IP address of incoming email messages may trust emails sent through your ISP more than emails that you send directly yourself. (Especially if your IP address is considered "residential.") Then the problem shifts to convincing your ISP that you're not a spammer, with 1k emails per day.
There are many services that provide SMTP. Alexus provided one, but it's pretty much a commodity, so shop around. These normally charge you based on how many emails you send in a given amount of time.
Another possibility is to get a VPS and set up a mailserver on it. (Taking care to secure it properly. Spammers love these.) Then you're charged for bandwidth and storage space rather than per email. For example, Linode offers clean IP addresses (not blackholed) with hundreds of gigabytes of bandwidth per month. You can send a lot of emails that way for cheap.
Yet another way to go, if your PHP web app is a mailing list management app, is to outsource the mailing list functionality to someplace like Constant Contact. Then you greatly simplify your infrastructure and probably even gain features.
One more thing to add is that if you're getting tagged as a spammer, you may not have your DNS setup correctly. I beleive an srv record is what's needed here.
