Obsolescence management is as much art as science (sometimes I wish there really was a crystal ball available).
Is it true that DIP chips and ICs are going to be obsolete in the near
At the risk of trying to see into the future by looking at past and current trends, I really don't think so; existing parts may slowly drop DIP packaging but it all depends on sales. Some manufacturers are better than others in this regard and those that support really long lifecycles (avionics comes to mind with the 30 year or more life for some pieces of equipment) will not necessarily EOL parts although the lead times may get rather long (1 batch manufactured per year in some cases).
New parts are not often offered in DIP packages (although those with die revisions have usually maintained the availability of most package styles). There are some parts where SMT packaging is the only viable solution (see this question for an example).
Some new parts are available in DIP packaging if they are an 'improved' (manufacturer marketing speak) device designed to replace existing parts.
Note that you can still buy the venerable 741 op amp from a number of sources; this part is still going strong after several decades in through hole packaging. This part was first manufactured in 1963 so there are some parts that never appear to die.
Is it wise to consider the SMD packages for development starting 2020?
For eg, will DIP versions of MCP3004/8 or ULN chips go extinct shortly
(in the coming 5 years) and decision should be taken to move to SMD
versions of the same?
As noted, some manufacturers are better than others in this regard; as noted in the comments, new designs should really go with a SMT package style (because that is generally where the sales for the manufacturer will be for various reasons, physical size and increased part density among them).
I am not against DIP packages for ICs although I have not used one in a completely new design in over 20 years.
Moreover, irrespective of the chips, is there a way to predict or get
notified as to when the chips will be made obsolete?
Yes, in many cases. You can sign up to product notification emails (there is usually a link on the product / family web page to do this) for the majority of parts from many manufacturers (but notably not for the majority of Chinese ones), but beware; notifications come out for a multitude of reasons and you can quickly submerge under a barrage of such notifications. That said, it is useful to get these as it helps understand which parts are likely to become obsolete.
At one place I worked, I was the central technical point of contact for all electronics and I set up a separate email account specifically for notifications - in avionics (particularly safety critical) even a particular die revision being discontinued is a major issue, and I have seen updated parts (micro controllers) with new die revisions need major software surgery to make them operate as the original.
Having a good idea of where the market was moving influenced our design choices.
There are other (paid) resources available, such as Silicon Expert and Ciiva (now part of Altium) (I am not endorsing them, these are just examples) which provide reasonable predictions based on a number of factors.
Perhaps one of the most difficult types of part to predict is FPGAs; the usual suspects only list them as 'production' and the intelligence tools say they will be around for at least 2 years. In reality, the lifecycle of most FPGAs is about 15 to 20 years (at least from Xilinx); this is where being on the product notification list is very strongly suggested (be prepared to read through a list of hundreds of affected parts as it is usually a family of parts that go EOL / NRND).
As also noted, look around the distribution chain; statements of 'in production' coupled with 'unavailable' are a red flag.
Datasheets where the status is still 'preliminary' after a year or so is another huge red flag.
Yes, you can protect yourself to a certain extent; something I have not yet noted is that some manufacturers operate 'extended availability' programmes (which varies from 7 to 15 years guaranteed availability) and then there is at least one (well, before they were subsumed by Analog Devices but I hope the policy remains) where the corporate policy was to never obsolete a die (which is why they are so popular in the avionics and other long lifecycle industries).
I have seen some complex devices (GPUs in particular) become EOL before the design cycle was complete.
Obsolescence management requires a multi-pronged approach; there is no simple or single answer.